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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $0$ 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.


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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
PII: S 0002-9939(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