Homology, Homotopy and Applications

Defining relations for classical Lie superalgebras without Cartan matrices

P. Grozman, D. Leites, and E. Poletaeva

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The analogs of Chevalley generators are offered for simple (and close to them) $\Zee$-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 presentations [sic!] of exceptional Lie superalgebras and Lie superalgebras of hamiltonian vector fields.

Article information

Homology Homotopy Appl., Volume 4, Number 2 (2002), 259-275.

First available in Project Euclid: 13 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B20: Simple, semisimple, reductive (super)algebras
Secondary: 17B25: Exceptional (super)algebras 17B66: Lie algebras of vector fields and related (super) algebras 17B70: Graded Lie (super)algebras


Grozman, P.; Leites, D.; Poletaeva, E. Defining relations for classical Lie superalgebras without Cartan matrices. Homology Homotopy Appl. 4 (2002), no. 2, 259--275. https://projecteuclid.org/euclid.hha/1139852465

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