Defining relations for classical Lie superalgebras without Cartan matrices

Abstract

The analogs of Chevalley generators are oered for simple (and close to them)Z-graded complex Lie algebras and Lie su- peralgebras of polynomial growth without Cartan matrix. We show how to derive the deÞning relations between these gener- ators and explicitly write them for a most natural (distin- guished 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 presentations of excep- tional Lie superalgebras and Lie superalgebras of hamiltonian vector Þelds. To Jan-Erik Roos on his sixty-Þfth birthday