Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

Defining relations for classical Lie superalgebras without Cartan matrices

Pages: 259 – 275

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n2.a12

Authors

P. Grozman (Department of Mathematics, University of Stockholm, Sweden)

D. Leites (Department of Mathematics, University of Stockholm, Sweden)

E. Poletaeva (Department of Mathematics, Lund University, Sweden)

Abstract

The analogs of Chevalley generators are offered for simple (and close to them) $\mathbb{Z}$-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.

Keywords

Lie superalgebras, defining relations

2010 Mathematics Subject Classification

17A70, 17B01, 17B70

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