Some new simple modular Lie superalgebras

Alberto Elduque

Vol. 231 (2007), No. 2, 337–359

DOI: 10.2140/pjm.2007.231.337

Abstract

Two new simple modular Lie superalgebras will be obtained in characteristics $3$ and $5$, which share the property that their even parts are orthogonal Lie algebras and the odd parts their spin modules. The characteristic $5$ case will be shown to be related, by means of a construction of Tits, to the exceptional ten-dimensional Jordan superalgebra of Kac.

Keywords

Lie superalgebra, Kac Jordan superalgebra, spin module

Mathematical Subject Classification 2000

Primary: 17B50

Secondary: 17B60

Milestones

Received: 30 December 2005

Accepted: 17 April 2006

Published: 1 June 2007