Infinite-dimensional Lie algebras

of generalized Block type

Authors:
J. Marshall Osborn and Kaiming Zhao

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1641-1650

MSC (1991):
Primary 17B40, 17B65, 17B66, 17B68, 17B70

Published electronically:
February 18, 1999

MathSciNet review:
1486746

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Abstract | References | Similar Articles | Additional Information

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

**[B1]**Richard Block,*New simple Lie algebras of prime characteristic*, trans. Amer. Math. Soc.**89**(1958), 421–449. MR**0100010**, 10.1090/S0002-9947-1958-0100010-8**[B2]**Richard Block,*On torsion-free abelian groups and Lie algebras*, Proc. Amer. Math. Soc.**9**(1958), 613–620. MR**0097444**, 10.1090/S0002-9939-1958-0097444-2**[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.

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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:
http://dx.doi.org/10.1090/S0002-9939-99-04811-X

Received by editor(s):
September 23, 1997

Published electronically:
February 18, 1999

Communicated by:
Lance W. Small

Article copyright:
© Copyright 1999
American Mathematical Society