Abstract
In this paper we consider generalized Lie algebra structures on graded associative algebras. We are interested in the situation where such structures are solvable and even commutative. We first prove some theorems in the case of solvable structures on semiprime, prime or simple associative algebras. Then we describe finite-dimensional associative algebras over an algebraically closed field of characteristic zero graded by a finite elementary abelian group which are generalized commutative under a skew-symmetric bicharacter on the grading group.
The first author kindly acknowledges a support by MUN Dean of Science Research Grant #38647 and NSERC grant No. 227060-00.
The second author kindly acknowledges a support by NSF grant DMS 01-00461.
The third author kindly acknowledges a support by RFBR, grants 02-01-00219 and 00-15-96128.
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© 2003 Kluwer Academic Publishers
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Bahturin, Y., Montgomery, S., Zaicev, M. (2003). Generalized Lie Solvability of Associative Algebras. In: Bahturin, Y. (eds) Groups, Rings, Lie and Hopf Algebras. Mathematics and Its Applications, vol 555. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0235-3_1
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DOI: https://doi.org/10.1007/978-1-4613-0235-3_1
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