On Lie and associative algebras containing inner derivations

Details On Lie and associative algebras containing inner derivations On Lie and associative algebras containing inner derivations

2012-04-23

arxiv.org/abs/1204.5216v1

Mathematics

Rings and Algebras

11 pages, accepted for publication in Linear Algebra Appl

Scientific paper

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 $A$.

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