Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 014, 17 pages      math.QA/0210264      https://doi.org/10.3842/SIGMA.2009.014
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Simple Finite Jordan Pseudoalgebras

Pavel Kolesnikov
Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Received September 12, 2008, in final form January 10, 2009; Published online January 30, 2009

Abstract
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.

Key words: Jordan pseudoalgebra; conformal algebra; TKK-construction.

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