Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Infinite-dimensional Lie algebras of generalized Block type

Author(s): J. Marshall Osborn; Kaiming Zhao
Journal: Proc. Amer. Math. Soc. 127 (1999), 1641-1650.
MSC (1991): Primary 17B40, 17B65, 17B66, 17B68, 17B70
Posted: February 18, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: This paper investigates a class of infinite-dimensional Lie algebras over a field of characteristic $0$ 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 $K$ Lie algebras and some Lie algebras of generalized Cartan type $H$, and a second one is the class of Lie algebras of type $L$, which were previously defined and studied elsewhere by the authors. The other three types are hybrids of the first two types, and are new.

References:

[B1]
R. Block, New simple Lie algebras of prime characteristic, Trans. Amer. Math. Soc., 72(1958), 421-449. MR 20:6446

[B2]
R. Block, On torsion-free abelian groups and Lie algebras, Proc. Amer. Math. Soc., 9(1958), 613-620. MR 20:3913

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

[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.
[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.

[OZ2]
J.M. Osborn and K. Zhao, Generalized Cartan type K Lie algebras in characteristic 0, Comm. Alg., 25(1997), 3325-3360. CMP 97:17
[OZ3]
J.M. Osborn and K. Zhao, Infinite dimensional Lie algebras of type L, preprint, 1997.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 17B40, 17B65, 17B66, 17B68, 17B70

Retrieve articles in all Journals with MSC (1991): 17B40, 17B65, 17B66, 17B68, 17B70

Additional Information:

J. Marshall Osborn
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: osborn@math.wisc.edu

Kaiming Zhao
Affiliation: Institute of Systems Science, Academia Sinica, Beijing, 100080, China
Email: zhao@iss06.iss.ac.cn, zhao@math.wisc.edu

DOI: 10.1090/S0002-9939-99-04811-X
PII: S 0002-9939(99)04811-X
Received by editor(s): September 23, 1997
Posted: February 18, 1999
Communicated by: Lance W. Small
Copyright of article: Copyright 1999, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google