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# 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: https://dx.doi.org/10.4310/HHA.2002.v4.n2.a12

#### Authors

#### 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

Published 1 January 2002