University of Birmingham > Talks@bham > Algebra Seminar > The Generalised Nilradical of a Lie Algebra

The Generalised Nilradical of a Lie Algebra

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A solvable Lie algebra L has the property that its nilradical N contains its own centraliser. This is interesting because it gives a representation of L as a subalgebra of the derivation algebra of its nilradical, with kernel equal to the centre of N. I will consider several possible generalisations of the nilradical for which this property holds in any Lie algebra. The main result states that for every Lie algebra L, L/Z(N), where Z(N) is the centre of the nilradical of L, is isomorphic to a subalgebra of Der(N*) where N* is an ideal of L such that N*/N is the socle of a semisimple Lie algebra.

This talk is part of the Algebra Seminar series.

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