Abstract
In one of our recent papers, the associative and the Lie algebras of Weyl typeA[D]=A⊗F[D] were defined and studied, whereA is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebraD ofA. In the present paper, a class of the above associative and Lie algebrasA[D] with F being a field of characteristic 0,D consisting of locally finite but not locally nilpotent derivations ofA, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kawamoto, N., Generalizations of Witt algebras over a field of characteristic zero, Hiroshima Math. J., 1985, 16: 417–462.
Osborn, J. M., New simple infinite-dimensional Lie algebras of characteristic O, J. Alg., 1996, 185: 820–835.
Dokovic, D. Z., Zhao, K., Derivations, isomorphisms, and second cohomology of generalized Witt algebras, Trans. Amer. Math. Soc., 1998, 350(2): 643–664.
Dokovic, D. Z., Zhao, K., Generalized Cartan type W Lie algebras in characteristic zero, J. Alg., 1997, 195: 170–210.
Dokovic, D. Z., Zhao, K., Derivations, isomorphisms, and second cohomology of generalized Block algebras, Alg. Colloq., 1996, 3(3): 245–272.
Osborn, J. M., Zhao, K., Generalized Poisson bracket and Lie algebras of type H in characteristic O, Math. Z., 1999, 230: 107–143.
Osborn, J. M., Zhao, K., Generalized Cartan type K Lie algebras in characteristic O, Comm. Alg., 1997, 25: 3325–3360.
Zhao, K., Isomorphisms between generalized Cartan type W Lie algebras in characteristic zero, Canadian J. Math., 1998, 50: 210–224.
Passman, D. P., Simple Lie algebras of Witt type, J. Alg., 1998, 206: 682–692.
Jordan, D. A., On the simplicity of Lie algebras of derivations of commutative algebras, J. Alg., 2000, 228: 580–585.
Xu, X., New generalized simple Lie algebras of Cartan type over a field with characteristic O, J. Alg., 2000, 224: 23–58.
Su, Y., Xu, X., Zhang, H., Derivation-simple algebras and the structures of Lie algebras of Witt type, J. Alg., 2000, 233: 642–662.
Su, Y., Zhao, K., Second cohomology group of generalized Witt type Lie algebras and certain representations, Comm. Algebra, to appear.
Su, Y., Zhao, K., Simple algebras of Weyl type, Science in China, Ser. A, 2001, 44(4): 419–426.
Zhao, K., Simple algebras of Weyl type II, Proc. Amer. Math. Soci., 130(2002), 1323-1332.
Zhao, K., Automorphisms of algebras of differential operators, J. of Capital Normal University, 1994, 1: 1–8.
Zhao, K., Lie algebra of derivations of algebras of differential operators, Chinese Science Bulletin, 1993, 38(10): 793–798.
Bresar, M., Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc., 1993, 335(2): 525–546.
Malm, D. R., Simplicity of partial and Schmidt differential rings, Pacific J. Math., 1988, 132: 85–112.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Su, Y., Zhao, K. Isomorphism classes and automorphism groups of algebras of Weyl type. Sci. China Ser. A-Math. 45, 953–963 (2002). https://doi.org/10.1007/BF02879978
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02879978