1. On Lie and associative algebras containing inner derivations
- Author
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Matej Brešar, Špela Špenko, Mathematics, and Algebra
- Subjects
Pure mathematics ,Numerical Analysis ,Algebra and Number Theory ,Subalgebra ,Universal enveloping algebra ,Mathematics - Rings and Algebras ,Matrix algebra ,Lie conformal algebra ,Graded Lie algebra ,Algèbre - théorie des anneaux - théorie des corps ,Filtered algebra ,Division algebra ,Algebra representation ,Prime algebra ,Cellular algebra ,Discrete Mathematics and Combinatorics ,Inner derivation ,Geometry and Topology ,Lie Algebra ,Mathematics - Representation Theory ,Mathematics - Abstract
We describe subalgebras of the Lie algebra $\mf{gl}(n^2)$ that contain all inner derivations of $A=M_n(F)$ (where $n\ge 5$ and $F$ is an algebraically closed field of characteristic 0). In a more general context where $A$ is a prime algebra satisfying certain technical restrictions, we establish a density theorem for the associative algebra generated by all inner derivations of $A$., Comment: 11 pages, accepted for publication in Linear Algebra Appl
- Published
- 2012
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