Erlangen Program at Large-1: Geometry of Invariants
This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL₂(R) group. We describe here geometries of corresponding domains. The principal rôle is played by Cliff...
Збережено в:
| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146514 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Erlangen Program at Large-1: Geometry of Invariants / V.V. Kisil // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 73 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1465142019-02-10T01:25:06Z Erlangen Program at Large-1: Geometry of Invariants Kisil, V.V. This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL₂(R) group. We describe here geometries of corresponding domains. The principal rôle is played by Clifford algebras of matching types. In this paper we also generalise the Fillmore-Springer-Cnops construction which describes cycles as points in the extended space. This allows to consider many algebraic and geometric invariants of cycles within the Erlangen program approach. 2010 Article Erlangen Program at Large-1: Geometry of Invariants / V.V. Kisil // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 73 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30G35; 22E46; 30F45; 32F45 DOI:10.3842/SIGMA.2010.076 http://dspace.nbuv.gov.ua/handle/123456789/146514 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL₂(R) group. We describe here geometries of corresponding domains. The principal rôle is played by Clifford algebras of matching types. In this paper we also generalise the Fillmore-Springer-Cnops construction which describes cycles as points in the extended space. This allows to consider many algebraic and geometric invariants of cycles within the Erlangen program approach. |
| format |
Article |
| author |
Kisil, V.V. |
| spellingShingle |
Kisil, V.V. Erlangen Program at Large-1: Geometry of Invariants Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kisil, V.V. |
| author_sort |
Kisil, V.V. |
| title |
Erlangen Program at Large-1: Geometry of Invariants |
| title_short |
Erlangen Program at Large-1: Geometry of Invariants |
| title_full |
Erlangen Program at Large-1: Geometry of Invariants |
| title_fullStr |
Erlangen Program at Large-1: Geometry of Invariants |
| title_full_unstemmed |
Erlangen Program at Large-1: Geometry of Invariants |
| title_sort |
erlangen program at large-1: geometry of invariants |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146514 |
| citation_txt |
Erlangen Program at Large-1: Geometry of Invariants / V.V. Kisil // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 73 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kisilvv erlangenprogramatlarge1geometryofinvariants |
| first_indexed |
2023-05-20T17:24:58Z |
| last_indexed |
2023-05-20T17:24:58Z |
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1796153238334996480 |