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CB-degenerations and rigid degenerations of algebras

100%

Hajduk A.

Colloquium Mathematicum

2006

tom 106

nr 2

305-310

The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.

Two classes of almost Galois coverings for algebras

63%

Dowbor P. , Hajduk A.

Colloquium Mathematicum

2012

tom 127

nr 2

253-298

We prove that for any representation-finite algebra A (in fact, finite locally bounded k-category), the universal covering F: Ã → A is either a Galois covering or an almost Galois covering of integral type, and F admits a degeneration to the standard Galois covering F̅: Ã→ Ã/G, where $G = Π(Γ_A)$ is the fundamental group of $Γ_A$. It is shown that the class of almost Galois coverings F: R → R' of integral type, containing the series of examples from our earlier paper [Bol. Soc. Mat. Mexicana 17 (2011)], behaves much more regularly than usual with respect to the standard properties of the pair $(F_λ, F_•)$ of adjoint functors associated to F.