On Lie and associative algebras containing inner derivations

2012/04/23 by Brešar, M., Špenko, Š.
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1204.5216

Abstract

We describe subalgebras of the Lie algebra \mfgl(n²) that contain all inner derivations of A=M_n(F) (where n≥ 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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