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Simple Finite Jordan Pseudoalgebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Simple Finite Jordan Pseudoalgebras
Інший ID:
2000 Mathematics Subject Classification: 17C50; 17B60; 16W30
Посилання:
Simple Finite Jordan Pseudoalgebras / P. Kolesnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. I am very grateful to L.A. Bokut, I.V. L’vov, E.I. Zel’manov, and V.N. Zhelyabin for their interest in the present work and helpful discussions. It is my pleasure to appreciate the ef forts of the referees, whose suggestions and comments helped me to make the paper readable. The work was partially supported by SSc-344.2008.1. I gratefully acknowledge the support of the Pierre Deligne fund based on his 2004 Balzan prize in mathematics, and Novosibirsk City Administration grant of 2008.
Дата:
2009
Переглядів:
390
Завантажень:
213
Анотація:
We consider the structure of Jordan H-pseudoalgebras which are linearly finitely generated over a Hopf algebra H. There are two cases under consideration: H = U(h) and H = U(h) # C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits-Kantor-Koecher construction for finite Jordan pseudoalgebras and describe all simple ones.
