Defining relations for classical Lie superalgebras without Cartan matrices

Details Defining relations for classical Lie superalgebras without Cartan matrices Defining relations for classical Lie superalgebras without Cartan matrices

2002-02-18

arxiv.org/abs/math/0202152v1

In: E. Ivanov et. al. (eds.) Supersymmetries and Quantum Symmetries (SQS'99, 27--31 July, 1999), Dubna, JINR, 2000, 387--396;

Mathematics

Representation Theory

13p., Latex (this is an expanded version of the SQS'99 talk)

Scientific paper

The analogs of Chevalley generators are offered for simple (and close to them) Z-graded complex Lie algebras and Lie superalgebras of polynomial growth without Cartan matrix. We show how to derive the defining relations between these generators and explicitly write them for a "most natural" ("distinguished" in terms of Penkov and Serganova) system of simple roots. The results are given mainly for Lie superalgebras whose component of degree zero is a Lie algebra (other cases being left to the reader). Observe presentations of exceptional Lie superalgebras and Lie superalgebras of hamiltonian vector fields. Now we can, at last, q-quantize the Lie Lie superalgebras of hamiltonian vector fields and Poisson superalgebras.

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