arXiv subjects

Yuriy A. Drozd

Publications and source records attributed to Yuriy A. Drozd.

24 records · Page 2Linked to original sources

arXiv2004

Dimensions of finite type for representations of partially ordered sets

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms.

math.RT↗

arXiv2004

Matrix problems and stable homotopy types of polyhedra

It is a survey of the results on the classification of stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author. The proofs are based on the technique of matrix problems (bimodule categories).

math.AT↗

arXiv2003

Vector bundles and Cohen-Macaulay modules

This survey presents some recent results of G.-M.Greuel and the author on vector bundles over algebraic curves and on Cohen-Macaulay modules over surface singularities. It is mainly devoted to the classification problems, especially to the tame-wild dichotomy and to the description of vector bundles and Cohen-Macaulay modules in the tame cases.

math.AG↗

arXiv2003

Tame-wild dichotomy for derived categories

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular, that any degeneration of a derived wild algebra is derived wild; respectively, any deformation of a derived tame algebra is derived tame.

math.RT↗

arXiv2003

Derived tame and derived wild algebras

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.

math.RT↗

arXiv2002

Semi-Continuity for Derived Categories

We prove that the number of parameters defining a complex of projective modules over a finite dimensional algebra is upper semi-continuous in families of algebras. Supposing that every algebra is either derived tame or derived wild, we get that a degeneration of a derived wild algebra is derived wild too. We also explain why the so-called counter-example of Bruestle is in fact not a counter-example.

math.RT↗