Infinitedimensional Lie algebras of generalized Block type
Authors:
J. Marshall Osborn and Kaiming Zhao
Journal:
Proc. Amer. Math. Soc. 127 (1999), 16411650
MSC (1991):
Primary 17B40, 17B65, 17B66, 17B68, 17B70
Published electronically:
February 18, 1999
MathSciNet review:
1486746
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: This paper investigates a class of infinitedimensional 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 (20 #6446), http://dx.doi.org/10.1090/S00029947195801000108
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Richard
Block, On torsionfree abelian groups and Lie
algebras, Proc. Amer. Math. Soc. 9 (1958), 613–620. MR 0097444
(20 #3913), http://dx.doi.org/10.1090/S00029939195800974442
 [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), 33253360. CMP 97:17
 [OZ3]
J.M. Osborn and K. Zhao, Infinite dimensional Lie algebras of type L, preprint, 1997.
 [B1]
 R. Block, New simple Lie algebras of prime characteristic, Trans. Amer. Math. Soc., 72(1958), 421449. MR 20:6446
 [B2]
 R. Block, On torsionfree abelian groups and Lie algebras, Proc. Amer. Math. Soc., 9(1958), 613620. 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), 33253360. 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/S000299399904811X
PII:
S 00029939(99)04811X
Received by editor(s):
September 23, 1997
Published electronically:
February 18, 1999
Communicated by:
Lance W. Small
Article copyright:
© Copyright 1999
American Mathematical Society
