Noncommutative Algebraic Geometry and Representations of Quantized Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
330 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others |
| Beschreibung: | 1 Online-Ressource (XII, 322 p) |
| ISBN: | 9789401584302 9789048145775 |
| DOI: | 10.1007/978-94-015-8430-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424057 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1995 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401584302 |c Online |9 978-94-015-8430-2 | ||
| 020 | |a 9789048145775 |c Print |9 978-90-481-4577-5 | ||
| 024 | 7 | |a 10.1007/978-94-015-8430-2 |2 doi | |
| 035 | |a (OCoLC)1165505638 | ||
| 035 | |a (DE-599)BVBBV042424057 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.46 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Rosenberg, Alexander L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Noncommutative Algebraic Geometry and Representations of Quantized Algebras |c by Alexander L. Rosenberg |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1995 | |
| 300 | |a 1 Online-Ressource (XII, 322 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 330 | |
| 500 | |a This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Topological Groups | |
| 650 | 4 | |a Associative Rings and Algebras | |
| 650 | 4 | |a Topological Groups, Lie Groups | |
| 650 | 4 | |a Category Theory, Homological Algebra | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Nichtkommutative Algebra |0 (DE-588)4304013-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtkommutative Algebra |0 (DE-588)4304013-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-015-8430-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859474 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100540313600 |
|---|---|
| any_adam_object | |
| author | Rosenberg, Alexander L. |
| author_facet | Rosenberg, Alexander L. |
| author_role | aut |
| author_sort | Rosenberg, Alexander L. |
| author_variant | a l r al alr |
| building | Verbundindex |
| bvnumber | BV042424057 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165505638 (DE-599)BVBBV042424057 |
| dewey-full | 512.46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.46 |
| dewey-search | 512.46 |
| dewey-sort | 3512.46 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8430-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03310nmm a2200505zcb4500</leader><controlfield tag="001">BV042424057</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1995 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401584302</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-015-8430-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048145775</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-4577-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-015-8430-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165505638</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424057</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.46</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rosenberg, Alexander L.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Noncommutative Algebraic Geometry and Representations of Quantized Algebras</subfield><subfield code="c">by Alexander L. Rosenberg</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 322 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">330</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological Groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Associative Rings and Algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological Groups, Lie Groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Category Theory, Homological Algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtkommutative Algebra</subfield><subfield code="0">(DE-588)4304013-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtkommutative Algebra</subfield><subfield code="0">(DE-588)4304013-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-015-8430-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859474</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042424057 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401584302 9789048145775 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859474 |
| oclc_num | 1165505638 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 322 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Rosenberg, Alexander L. Verfasser aut Noncommutative Algebraic Geometry and Representations of Quantized Algebras by Alexander L. Rosenberg Dordrecht Springer Netherlands 1995 1 Online-Ressource (XII, 322 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 330 This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others Mathematics Algebra Topological Groups Associative Rings and Algebras Topological Groups, Lie Groups Category Theory, Homological Algebra Applications of Mathematics Mathematik Nichtkommutative Algebra (DE-588)4304013-5 gnd rswk-swf Nichtkommutative Algebra (DE-588)4304013-5 s 1\p DE-604 https://doi.org/10.1007/978-94-015-8430-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rosenberg, Alexander L. Noncommutative Algebraic Geometry and Representations of Quantized Algebras Mathematics Algebra Topological Groups Associative Rings and Algebras Topological Groups, Lie Groups Category Theory, Homological Algebra Applications of Mathematics Mathematik Nichtkommutative Algebra (DE-588)4304013-5 gnd |
| subject_GND | (DE-588)4304013-5 |
| title | Noncommutative Algebraic Geometry and Representations of Quantized Algebras |
| title_auth | Noncommutative Algebraic Geometry and Representations of Quantized Algebras |
| title_exact_search | Noncommutative Algebraic Geometry and Representations of Quantized Algebras |
| title_full | Noncommutative Algebraic Geometry and Representations of Quantized Algebras by Alexander L. Rosenberg |
| title_fullStr | Noncommutative Algebraic Geometry and Representations of Quantized Algebras by Alexander L. Rosenberg |
| title_full_unstemmed | Noncommutative Algebraic Geometry and Representations of Quantized Algebras by Alexander L. Rosenberg |
| title_short | Noncommutative Algebraic Geometry and Representations of Quantized Algebras |
| title_sort | noncommutative algebraic geometry and representations of quantized algebras |
| topic | Mathematics Algebra Topological Groups Associative Rings and Algebras Topological Groups, Lie Groups Category Theory, Homological Algebra Applications of Mathematics Mathematik Nichtkommutative Algebra (DE-588)4304013-5 gnd |
| topic_facet | Mathematics Algebra Topological Groups Associative Rings and Algebras Topological Groups, Lie Groups Category Theory, Homological Algebra Applications of Mathematics Mathematik Nichtkommutative Algebra |
| url | https://doi.org/10.1007/978-94-015-8430-2 |
| work_keys_str_mv | AT rosenbergalexanderl noncommutativealgebraicgeometryandrepresentationsofquantizedalgebras |