Group gradings on restricted Cartan-type Lie algebras

Yuri Bahturin and Mikhail Kochetov

Vol. 253 (2011), No. 2, 289–319

DOI: 10.2140/pjm.2011.253.289

Abstract

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1 ) and S(m;1 ) for m ≥ 2, in terms of numerical and group-theoretical invariants. Our main tool is automorphism group schemes, which we determine for the simple restricted Lie algebras of types S(m;1 ) and H(m;1 ). The ground field is assumed to be algebraically closed of characteristic p > 3.

Keywords

graded algebra, simple Lie algebra, grading, Cartan-type Lie algebra

Mathematical Subject Classification 2000

Primary: 17B70

Secondary: 17B60

Milestones

Received: 28 July 2010

Accepted: 27 April 2011

Published: 21 January 2012