Leírás
I will discuss the problem of classification of pencils of Lie algebra
structures, one of which is semisimple, and the approach to it presented
in my paper "Compatible Lie brackets: Towards a classification"(Journal
of Lie Theory, 24(2014), 561-623). Any such pencil is determined by a
linear operator which is defined up to the addition of a derivation. A
special fixing of this operator is introduced to get rid of this
ambiguity and the operators preserving the root decomposition with
respect to a Cartan subalgebra are considered. The classification leads
to two disjoint classes of pairs depending on the symmetry properties
of the corresponding operator with respect to the Killing form. In the end
the list of related open problems will be presented.