Generalized Vertex Algebras and Relative Vertex Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1993
|
| Schriftenreihe: | Progress in Mathematics
112 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate one-dimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics |
| Beschreibung: | 1 Online-Ressource (IX, 206 p) |
| ISBN: | 9781461203537 9781461267218 |
| DOI: | 10.1007/978-1-4612-0353-7 |
Internformat
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| 490 | 0 | |a Progress in Mathematics |v 112 | |
| 500 | |a The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate one-dimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics | ||
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| 650 | 4 | |a Algebra | |
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| 650 | 4 | |a Topological Groups | |
| 650 | 4 | |a Operator theory | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Dong, Chongying |
| author_facet | Dong, Chongying |
| author_role | aut |
| author_sort | Dong, Chongying |
| author_variant | c d cd |
| building | Verbundindex |
| bvnumber | BV042419513 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)906733885 (DE-599)BVBBV042419513 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0353-7 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461203537 9781461267218 |
| language | English |
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| publishDate | 1993 |
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| publisher | Birkhäuser Boston |
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| series2 | Progress in Mathematics |
| spelling | Dong, Chongying Verfasser aut Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong, James Lepowsky Boston, MA Birkhäuser Boston 1993 1 Online-Ressource (IX, 206 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 112 The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate one-dimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics Mathematics Algebra Group theory Topological Groups Operator theory Associative Rings and Algebras Operator Theory Group Theory and Generalizations Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Mathematik Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Vertexoperator (DE-588)4188067-5 gnd rswk-swf Vertexalgebra (DE-588)4328736-0 gnd rswk-swf Vertexoperator (DE-588)4188067-5 s Verallgemeinerung (DE-588)4316262-9 s 1\p DE-604 Vertexalgebra (DE-588)4328736-0 s 2\p DE-604 Lepowsky, James Sonstige oth https://doi.org/10.1007/978-1-4612-0353-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dong, Chongying Generalized Vertex Algebras and Relative Vertex Operators Mathematics Algebra Group theory Topological Groups Operator theory Associative Rings and Algebras Operator Theory Group Theory and Generalizations Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Mathematik Verallgemeinerung (DE-588)4316262-9 gnd Vertexoperator (DE-588)4188067-5 gnd Vertexalgebra (DE-588)4328736-0 gnd |
| subject_GND | (DE-588)4316262-9 (DE-588)4188067-5 (DE-588)4328736-0 |
| title | Generalized Vertex Algebras and Relative Vertex Operators |
| title_auth | Generalized Vertex Algebras and Relative Vertex Operators |
| title_exact_search | Generalized Vertex Algebras and Relative Vertex Operators |
| title_full | Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong, James Lepowsky |
| title_fullStr | Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong, James Lepowsky |
| title_full_unstemmed | Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong, James Lepowsky |
| title_short | Generalized Vertex Algebras and Relative Vertex Operators |
| title_sort | generalized vertex algebras and relative vertex operators |
| topic | Mathematics Algebra Group theory Topological Groups Operator theory Associative Rings and Algebras Operator Theory Group Theory and Generalizations Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Mathematik Verallgemeinerung (DE-588)4316262-9 gnd Vertexoperator (DE-588)4188067-5 gnd Vertexalgebra (DE-588)4328736-0 gnd |
| topic_facet | Mathematics Algebra Group theory Topological Groups Operator theory Associative Rings and Algebras Operator Theory Group Theory and Generalizations Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Mathematik Verallgemeinerung Vertexoperator Vertexalgebra |
| url | https://doi.org/10.1007/978-1-4612-0353-7 |
| work_keys_str_mv | AT dongchongying generalizedvertexalgebrasandrelativevertexoperators AT lepowskyjames generalizedvertexalgebrasandrelativevertexoperators |