Quadratic Malcev Superalgebras with Reductive Even Part

Abstract

It is our goal to give an inductive description of quadratic Malcev superalgebras with reductive even part. We use the notion of double extension of Malcev superalgebras presented by Albuquerque and Benayadi in [4] and transfer to Malcev superalgebras the concept of generalized double extension given in [6] for Lie superalgebras.

Key Words:

• Malcev superalgebras
• Quadratic forms
• Reductive Malcev algebras

2000 Mathematics Subject Classification:

• 15A63
• 17A70

ACKNOWLEDGMENT

The authors would like to thank the referee for his helpful suggestions.

The first and the second authors acknowledge partial financial assistance by the CMUC, Department of Mathematics, University of Coimbra.

Notes

Communicated by A. Elduque.