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.
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