Almost semisimple algebras

Bounds for Bilinear Complexity of Noncommutative Group Algebras

We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show nontrivial lower bounds for the rest of the group algebras. These lower bounds are built on the top of Bläser’s results for semisimple algebras and algebras with ...

Semisimple Algebras of Almost Minimal Rank over the Reals

A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder–Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. We here start the investigation of the algebras for which the Alder–Strassen bound is off by one. As a first result, we completel...

Finite Dimensional Representations of W -algebras

W -algebras of finite type are certain finitely generated associative algebras closely related to universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete classification of finite dimensional irreducible modules for W -algebras. Also we get some partial results towards a conjecture by Ginzburg on their finite dimension...

Automatic continuity of surjective $n$-homomorphisms on Banach algebras

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras