Infinite-dimensional Lie algebras of generalized Block type
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- by J. Marshall Osborn and Kaiming Zhao PDF
- Proc. Amer. Math. Soc. 127 (1999), 1641-1650 Request permission
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
- Richard Block, New simple Lie algebras of prime characteristic, trans. Amer. Math. Soc. 89 (1958), 421–449. MR 0100010, DOI 10.1090/S0002-9947-1958-0100010-8
- Richard Block, On torsion-free abelian groups and Lie algebras, Proc. Amer. Math. Soc. 9 (1958), 613–620. MR 97444, DOI 10.1090/S0002-9939-1958-0097444-2
- D.Z. Djokovic and K. Zhao, Derivations, isomorphisms, and second cohomology of generalized Block algebras, Algebra Colloquium, Vol.3, 3(1996).
- D.Z. Djokovic and K. Zhao, Some infinite dimensional simple Lie algebras related to those of Block, J. Pure and Applied Algebra, in press.
- J.M. Osborn and K. Zhao, Generalized Poisson brackets and Lie algebras of type H in characteristic 0, Math. Z., 229(1998), No. 4.
- J.M. Osborn and K. Zhao, Generalized Cartan type K Lie algebras in characteristic 0, Comm. Alg., 25(1997), 3325-3360.
- J.M. Osborn and K. Zhao, Infinite dimensional Lie algebras of type L, preprint, 1997.
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
- Received by editor(s): September 23, 1997
- Published electronically: February 18, 1999
- Communicated by: Lance W. Small
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1641-1650
- MSC (1991): Primary 17B40, 17B65, 17B66, 17B68, 17B70
- DOI: https://doi.org/10.1090/S0002-9939-99-04811-X
- MathSciNet review: 1486746