Nonabelian multiplicative integration on surfaces:
"Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplica...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Co. Pte Ltd
c2016
|
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| Zusammenfassung: | "Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G. The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions. Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory — instead of the 2-categories and 2-functors that other authors prefer."-- |
| Beschreibung: | Title from PDF file title page (viewed September 9, 2015) |
| Beschreibung: | 1 online resource (xii, 173 p.) col. ill |
| ISBN: | 9814663859 9789814663854 |
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| 500 | |a Title from PDF file title page (viewed September 9, 2015) | ||
| 520 | |a "Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G. The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions. Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory — instead of the 2-categories and 2-functors that other authors prefer."-- | ||
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Datensatz im Suchindex
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| author | Yekutiely, Amnon |
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| author_sort | Yekutiely, Amnon |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.46 |
| dewey-search | 512/.46 |
| dewey-sort | 3512 246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044640637 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:58Z |
| institution | BVB |
| isbn | 9814663859 9789814663854 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030038609 |
| oclc_num | 918594087 988732249 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | 1 online resource (xii, 173 p.) col. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | World Scientific Publishing Co. Pte Ltd |
| record_format | marc |
| spelling | Yekutiely, Amnon Verfasser aut Nonabelian multiplicative integration on surfaces Amnon Yekutieli Non-abelian multiplicative integration on surfaces Singapore World Scientific Publishing Co. Pte Ltd c2016 1 online resource (xii, 173 p.) col. ill txt rdacontent c rdamedia cr rdacarrier Title from PDF file title page (viewed September 9, 2015) "Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G. The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions. Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory — instead of the 2-categories and 2-functors that other authors prefer."-- Noncommutative algebras Non-Abelian groups Surfaces, Algebraic Geometry, Algebraic Stokes-Integralsatz (DE-588)4759656-9 gnd rswk-swf Nichtkommutative Integrationstheorie (DE-588)4171743-0 gnd rswk-swf Nichtkommutative Integrationstheorie (DE-588)4171743-0 s Stokes-Integralsatz (DE-588)4759656-9 s 1\p DE-604 http://www.worldscientific.com/worldscibooks/10.1142/9537#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yekutiely, Amnon Nonabelian multiplicative integration on surfaces Noncommutative algebras Non-Abelian groups Surfaces, Algebraic Geometry, Algebraic Stokes-Integralsatz (DE-588)4759656-9 gnd Nichtkommutative Integrationstheorie (DE-588)4171743-0 gnd |
| subject_GND | (DE-588)4759656-9 (DE-588)4171743-0 |
| title | Nonabelian multiplicative integration on surfaces |
| title_alt | Non-abelian multiplicative integration on surfaces |
| title_auth | Nonabelian multiplicative integration on surfaces |
| title_exact_search | Nonabelian multiplicative integration on surfaces |
| title_full | Nonabelian multiplicative integration on surfaces Amnon Yekutieli |
| title_fullStr | Nonabelian multiplicative integration on surfaces Amnon Yekutieli |
| title_full_unstemmed | Nonabelian multiplicative integration on surfaces Amnon Yekutieli |
| title_short | Nonabelian multiplicative integration on surfaces |
| title_sort | nonabelian multiplicative integration on surfaces |
| topic | Noncommutative algebras Non-Abelian groups Surfaces, Algebraic Geometry, Algebraic Stokes-Integralsatz (DE-588)4759656-9 gnd Nichtkommutative Integrationstheorie (DE-588)4171743-0 gnd |
| topic_facet | Noncommutative algebras Non-Abelian groups Surfaces, Algebraic Geometry, Algebraic Stokes-Integralsatz Nichtkommutative Integrationstheorie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/9537#t=toc |
| work_keys_str_mv | AT yekutielyamnon nonabelianmultiplicativeintegrationonsurfaces |