  Since 2005 a new powerful invariant of an algebra emerged using earlier work
of Horv\'ath, H\'ethelyi, K\"ulshammer and Murray. The authors studied Morita
invariance of a sequence of ideals of the centre of a finite dimensional
algebra over a field of finite characteristic. It was shown that the sequence
of ideals is actually a derived invariant, and most recently a slightly
modified version of it 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 was given. This article surveys the results and gives some of the
constructions in more detail.
