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Gradings of non-graded Hamiltonian Lie algebras

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

A. Caranti  and
S. Mattarei
A. Caranti
Affiliation:
Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy, e-mail: caranti@science.unitn.it, mattarei@science.unitn.it
S. Mattarei
Affiliation:
Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy, e-mail: caranti@science.unitn.it, mattarei@science.unitn.it
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Abstract

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A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2: n; ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2: n; ω2) with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).

Keywords

Modular Lie algebrasgraded Lie algebrasderivationscentral extensionsloop algebras.

MSC classification

Secondary: 17B50: Modular Lie (super)algebras 17B70: Graded Lie (super)algebras 17B56: Cohomology of Lie (super)algebras 17B65: Infinite-dimensional Lie (super)algebras

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 399 - 440
Copyright
Copyright © Australian Mathematical Society 2005

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