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Some thin Lie algebras related to Albert-Frank algebras and algebras of maximal class

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

A. Caranti  and
S. Mattarei
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 e-mail: mattarei@science.unitn.it
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Abstract

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We investigate a class of infinite-dimensional, modular, graded Lie algebra in which the homogeneous components have dimension at most two. A subclass of these algebras can be obtained via a twisted loop algebra construction from certain finite-dimensional, simple Lie algebras of Albert-Frank type.

Another subclass of these algebras is strictly related to certain graded Lie algebras of maximal class, and exhibits a wide range of behaviours.

Keywords

modular Lie algebrasgraded Lie algebrasinfinite-dimensional Lie algebrascohomology of Lie algebras.

MSC classification

Secondary: 17B50: Modular Lie (super)algebras 17B70: Graded Lie (super)algebras 17B65: Infinite-dimensional Lie (super)algebras 17B68: Virasoro and related algebras 17B56: Cohomology of Lie (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 2 , October 1999 , pp. 157 - 184
Copyright
Copyright © Australian Mathematical Society 1999

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