Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Given a finite-dimensional algebra it belongs to one of the following classes: derived tame or derived wild algebras. In this thesis our aim is to determine which finite dimensional K-algebras with three simple modules are ...

We show that all unipotent classes in finite simple Chevalley or Steinberg groups, different from PSLn(q) and PSp2n(q), collapse (i.e. are never the support of a finite-dimensional Nichols algebra), with a possible exception ...

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective symplectic linear group over a finite field, corresponding to unipotent orbits, have infinite dimension. We give a criterion to deal ...

We give a cohomological characterization of the set of conjugacy classes of finite subgroups of the projective multiplicative group of a finite dimensional algebra that become conjugate to a given group over some finite ...

This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we ...