on the use of kulshammer type invariants in representation theory

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version of it is an invariant under stable equivalences of morita type. the invariant was used in various contexts to distinguish derived and stable equivalence classes of pairs of algebras in very subtle situations. generalisations to non symmetric algebras and to higher hochschild (co-)homology were given. this article surveys the results and gives some of the constructions in more details.