Jerzy Białkowski

Deformed preprojective algebras of generalized Dynkin type

We introduce the class of deformed preprojective algebras of generalized Dynkin graphs An (n > 1), D n (n > 4), EG, E 7 , Eg and L n (n ≥ 1) and prove that it coincides with the class of all basic connected finite-dimensional self-injective algebras for which the inverse Nakayama shift v -1 S of every non-projective simple module S is isomorphic to its third syzygy Ω 3 S.

Cartan matrices of selfinjective algebras of tubular type

AbstractThe Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten quiver consisting only of stable tubes has been shown to be the class of selfinjective algebras of tubular type, that is, the orbit algebras

Selfinjective algebras of tubular type

\hat B

On nonstandard tame selfinjective algebras having only periodic modules

/G of the repetitive algebras

Periodicity of self-injective algebras of polynomial growth

\hat B

Deformed preprojective algebras of generalized Dynkin type Ln: Classification and symmetricity

of tubular algebras B with respect to the actions of admissible groups G of automorphisms of