In the representation theory of finite groups, the stable equivalence of Morita type plays an important role. For general finite-dimensional algebras, this notion is still of particular interest. However, except for the class of self-injective algebras, one does not know much on the existence of such equivalences between two finite-dimensional algebras; in fact, even a nontrivial example is not...

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 modied version o...

The author is grateful for support from a PhD grant from the Engineering and Physical Sciences Research council of the UK and post-doctoral fellowship number SFRH/BPD/40762/2007 from the Fundação para a Ciéncia e a Tec-nologia of Portugal. This paper contains some work included in the authors PhD thesis ([5]). Abstract We introduce notions of compactness and weak compactness for multi-linear ma...

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps T : A → B between Banach algebras that are “close to multiplicative” in the following senses: the failure of multiplicativity, defined by ST (a, b) = T (a)T (b) − T (ab) (a, b ∈ A), is co...