Infinite-dimensional Lie algebras of generalized Block type-Reference-Cited by-同舟云学术

Infinite-dimensional Lie algebras of generalized Block type

Published:1999-02-18 Issue:6 Volume:127 Page:1641-1650
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Osborn J.,Zhao Kaiming

Abstract

This paper investigates a class of infinite-dimensional Lie algebras over a field of characteristic 0 0 which are called here Lie algebras of generalized Block type, and which genereralize a class of Lie algebras originally defined by Richard Block. Under certain natural restrictions, this class of Lie algebras is shown to break into five subclasses. One of these subclasses contains all generalized Cartan type K K Lie algebras and some Lie algebras of generalized Cartan type H H , and a second one is the class of Lie algebras of type L L , which were previously defined and studied elsewhere by the authors. The other three types are hybrids of the first two types, and are new.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1999-127-06/S0002-9939-99-04811-X/S0002-9939-99-04811-X.pdf

Reference7 articles.

1. New simple Lie algebras of prime characteristic;Block, Richard;trans. Amer. Math. Soc.,1958

2. On torsion-free abelian groups and Lie algebras;Block, Richard;Proc. Amer. Math. Soc.,1958

3. [DZ1] D.Z. Djokovic and K. Zhao, Derivations, isomorphisms, and second cohomology of generalized Block algebras, Algebra Colloquium, Vol.3, 3(1996).

4. [DZ2] D.Z. Djokovic and K. Zhao, Some infinite dimensional simple Lie algebras related to those of Block, J. Pure and Applied Algebra, in press.

5. [OZ1] J.M. Osborn and K. Zhao, Generalized Poisson brackets and Lie algebras of type H in characteristic 0, Math. Z., 229(1998), No. 4.

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