Matrix functions of bounded type: an interplay between function theory and operator theory
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Series: | Memoirs of the American Mathematical Society
volume 260, number 1253 (second of 5 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 100 Seiten |
| ISBN: | 9781470436247 |
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MARC
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| 245 | 1 | 0 | |a Matrix functions of bounded type |b an interplay between function theory and operator theory |c Raúl E. Curto, In Sung Hwang, Woo Young Lee |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2019] | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 260, number 1253 (second of 5 numbers) | |
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Record in the Search Index
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| adam_text | Contents Introduction Part 1. Basics xi 1 Chapter 1. Category Theory 1.1. Basics 1.2. Category equivalence 1.3. Terminal objects and kernel morphisms 1.4. Pointed categories 1.5. Rank 1 objects 1.6. Simplicity 3 3 4 5 5 7 Chapter 2. Quasigroups and Loops 2.1. Basics 2.2. Autotopisms and anti-autotopisins 2.3. Loop homomorphisms and the pointed category Loop* 2.4. Moufang loops and other loop varieties 2.5. Examples 9 9 Chapter 3. Latin Square Designs 3.1. Basics 3.2. Central Latin square designs 3.3. The correspondence between Mouf and CLSD 3.4. Cayley tables of groups 8 10 11 13 16 17 17 19 21 23 Chapter 4. Groups with Triality 4.1. Basics 4.2. Examples 4.3. Normal subgroups in the base group and wreath products 25 25 27 30 Part 2. 33 Equivalence Chapter 5. The Functor В 5.1. A presentation 5.2. The functor В 35 35 36 Chapter 6. Monies, Covers, and Isogeny in TriGrp 6.1. A fibered product 6.2. Monies in TriGrp 6.3. Covers and isogeny 39 39 40 40
vi CONTENTS Chapter 7. Universals and Adjoints 7.1. Universal and adjoint groups 7.2. Universal and adjoint categories 43 43 47 Chapter 8. 8.1. 8.2. Moufang Loops and Groups with Triality are Essentially the Same Thing 51 A category equivalence 51 Monies 53 Chapter 9. 9.1. 9.2. 9.3. Moufang Loops and Groups with Triality are Not Exactly the Same Thing Mouf and TriGrp are not equivalent Mouf* and TriGrp* are not equivalent Mouf* and ATriGrp* are not equivalent Part 3. 55 55 56 59 Related Topics 63 Chapter 10. The Functors S and M 10.1. S and S* 10.2. M and M* 65 65 66 Chapter 11.1. 11.2. 11.3. 11. The Functor G G and G* Properties of universal groups Another presentation 69 69 71 73 Chapter 12.1. 12.2. 12.3. 12. Multiplication Groups andAutotopisms Multiplication and inner mapping groups Autotopisms Moufang multiplication groups, nuclei, and special autotopisms 77 77 81 82 Chapter 13.1. 13.2. 13.3. 13.4. 13. Dora’s Approach Dora’s categories A presentation of the base group Equivalent presentations Moufang loops 87 87 91 97 98 Chapter 14.1. 14.2. 14.3. 14. Normal Structure Simplicity Short exact sequences Solvable Moufang loops 101 101 104 107 Chapter 15.1. 15.2. 15.3. 15.4. 15.5. 15. Some Related Categoriesand Objects З-nets Categories of conjugates Groups enveloping triality Tits’symmetric T-geometries Latin chamber systems covered by buildings 111 111 112 113 115 117
CONTENTS Part 4. Classical Triality vii 123 Chapter 16.1. 16.2. 16.3. 16.4. 16.5. 16. An Introduction to Concrete Triality Study’s triality Cartan’s triality Composition algebras and theoctonions Freudenthal’s triality Moufang loops from octonion algebras 125 125 126 126 127 127 Chapter 17.1. 17.2. 17.3. 17.4. 17.5. 17.6. 17. Orthogonal Spaces and Groups Orthogonal geometry Hyperbolic orthogonal spaces Oriflamme geometries Orthogonal groups Chevallcy groups Dn(F) Orthogonal groups in dimension 8 129 129 131 133 134 136 137 Chapter 18. Study’s and Cartan’s Triality 18.1. Triality geometries and Study’s triality 18.2. Cartan’s triality 139 139 143 Chapter 19.1. 19.2. 19.3. 19.4. 19.5. 19.6. 19. Composition Algebras Composition algebras General structure Hurwitz’ Theorem in a restricted version Doubling and Hurwitz’ Theorem in its general version Commuting and associating Algebraic triality for the split octonions 147 147 149 152 154 157 160 Chapter 20.1. 20.2. 20.3. 20. Freudenthal’s Triality Some calculations Freudenthal’s triality The spin kernel and spin group 163 163 164 167 Chapter 21.1. 21.2. 21.3. 21.4. 21. The Loop of Units in an Octonion Algebra Loop sections of octonion algebras Octonion multiplication and triality groups The split octonions Simple Moufang loops 171 171 174 176 177 Bibliography 179 Index 183
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| any_adam_object | 1 |
| author | Curto, Raúl E. 1954- Hwang, In Sung Lee, Woo Young |
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| id | DE-604.BV046179133 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:37:26Z |
| institution | BVB |
| isbn | 9781470436247 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031558700 |
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| physical | v, 100 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Curto, Raúl E. 1954- (DE-588)172707439 aut Matrix functions of bounded type an interplay between function theory and operator theory Raúl E. Curto, In Sung Hwang, Woo Young Lee Providence, Rhode Island American Mathematical Society [2019] © 2019 v, 100 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 260, number 1253 (second of 5 numbers) Hwang, In Sung aut Lee, Woo Young (DE-588)1294351737 aut Memoirs of the American Mathematical Society volume 260, number 1253 (second of 5 numbers) (DE-604)BV008000141 1253 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031558700&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Curto, Raúl E. 1954- Hwang, In Sung Lee, Woo Young Matrix functions of bounded type an interplay between function theory and operator theory Memoirs of the American Mathematical Society |
| title | Matrix functions of bounded type an interplay between function theory and operator theory |
| title_auth | Matrix functions of bounded type an interplay between function theory and operator theory |
| title_exact_search | Matrix functions of bounded type an interplay between function theory and operator theory |
| title_full | Matrix functions of bounded type an interplay between function theory and operator theory Raúl E. Curto, In Sung Hwang, Woo Young Lee |
| title_fullStr | Matrix functions of bounded type an interplay between function theory and operator theory Raúl E. Curto, In Sung Hwang, Woo Young Lee |
| title_full_unstemmed | Matrix functions of bounded type an interplay between function theory and operator theory Raúl E. Curto, In Sung Hwang, Woo Young Lee |
| title_short | Matrix functions of bounded type |
| title_sort | matrix functions of bounded type an interplay between function theory and operator theory |
| title_sub | an interplay between function theory and operator theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031558700&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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