Yuriy Drozd

$Research paper thumbnail of Cohen-Macaulay modules over the plane curve singularity of type $T_{44}$, II$

Cohen-Macaulay modules over the plane curve singularity of type $T_{44}$, II

Algebra and discrete mathematics, Oct 20, 2019

For a wide class of Cohen-Macaulay modules over the local ring of the plane curve singularity of ... more

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On the classification of vector bundles on projective curves

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Representations of nodal algebras of type E

Algebra and discrete mathematics, Apr 10, 2017

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Semicontinuity for representations of Cohen-Macaulay rings

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Letter of Ukrainian mathematicians

European Mathematical Society Magazine

On behalf of Ukrainian mathematicians, we would like to thank the EMS for the statement of solida... more On behalf of Ukrainian mathematicians, we would like to thank the EMS for the statement of solidarity published on March 2. At the same time, we are disappointed by the fact that the corporate membership of the two Russian mathematical societies, Moscow and St. Petersburg, wasn't suspended. The full-scale Russian invasion of Ukraine has been going on for almost a month. Every new day brings immense suffering and losses. The Russian troops destroy our country, they bomb hospitals, kindergartens, schools, and universities. The cruelty against civilians leaves us breathless. We are aware of the individual protests of the Russian mathematicians against the war. We appreciate the courage of those Russian colleagues who expressed their anti-war position publicly. Nevertheless, the majority of the Russian population continues to support the genocide against Ukrainian people. They are being spoiled by the mass media propaganda and cut from credible sources of information. In these conditions, it is important to reach the Russian people by all possible means, especially through the cultural and academic communities who may influence the public opinion in the country.

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Representation type of ^∞_λH_μ^1

For a semi-simple finite-dimensional complex Lie algebra g we classify the representation type of... more

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3 Representations of Nodal Algebras of Type a

We define nodal finite dimensional algebras and describe their structure over an algebraically cl... more We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness. 1991 Mathematics Subject Classification. 16G60, 16G10. Key words and phrases. representations of finite dimensional algebras, nodal algebras, gentle algebras, skewed-gentle algebras. 1 Recall that pure noetherian means noetherian without minimal submodules.

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Chernikov 2-Groups with Kleinian Top and Totally Reducible Bottom

Ukrainian Mathematical Journal, 2021

On Gelfand-Zetlin modules

On derived categories of certain associative algebras

Representations of Algebras and Related Topics, 2005

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Indecomposable homotopy types with at most two non-trivial homology groups

Contemporary Mathematics, 2001

On Schappert’s Characterization of Strictly Unimodal Plane Curve Singularities

Singularities, 1998

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Finite Dimensional Algebras

This English edition has an additional chapter "Elements of Homological Algebra". Homological met... more This English edition has an additional chapter "Elements of Homological Algebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only meticulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community.

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Hereditary orders

Ukrainian Mathematical Journal, 1969

Tame and Wild Two by Two Matrix Orders

Journal of Algebra, 1994

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Weight Modules over Generalized Weyl Algebras

Journal of Algebra, 1996

This work originated in an attempt to comprehend a striking likeness between representations and ... more

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Representation theory of homotopy types with at most two non-trivial homotopy groups localized at a prime

Mathematical Proceedings of the Cambridge Philosophical Society, 2000

ABSTRACT It is a classical result of Postnikov [15] that homotopy types X with at most two non-tr... more

Representation Type of H1

The Quarterly Journal of Mathematics, 2005

For a semi-simple finite-dimensional complex Lie algebra g, we classify the representation type o... more

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Simple vector bundles on plane degenerations of an elliptic curve

arXiv (Cornell University), Mar 28, 2009

In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this ... more In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles. 2000 Mathematics Subject Classification. Primary 16G60; Secondary 14H10 and 14H60. Key words and phrases. simple vector bundles and their moduli, degeneration of an elliptic curve, tame and wild, small reduction. We express our sincere thanks to Professor Serge Ovsienko for fruitful discussions and helpful advice. The first named author would like to thank the Mathematisches Forschungsinstitut Oberwolfach, where she stayed as a Leibniz fellow during the period that this paper was written. 1 In representation theory a category is called tame if its indecomposable objects can be described by some discrete and one continuous parameters, and wild if they are non-classifiable. An algebraic variety X is called vector-bundle-wild or vector-bundle-tame if the category VB X of vector bundles on X is wild or respectively tame (see ).

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Matrix problems, triangulated categories and stable homotopy types

arXiv (Cornell University), Mar 30, 2009

We show how the matrix problems can be used in studying triangulated categories. Then we apply th... more We show how the matrix problems can be used in studying triangulated categories. Then we apply the general technique to the classification of stable homotopy types of polyhedra, find out the "representation types" of such problems and give a description of stable homotopy types in finite and tame cases. Contents 1. Matrix problems arising in triangulated categories 2 2. Stable homotopy category 4 3. Discrete case: Whitehead-Chang Theorem 9 4. Tame case: Baues-Hennes Theorem 14 5. Torsion free polyhedra. Finite case 18 6. Torsion free polyhedra. Tame case 23 7. Wild cases 28 References 31 The technique of matrix problems, especially, of bimodule categories, has proved their efficiency in lots of problems from representation theory, algebraic geometry, group theory and other domains of modern algebra. During last years, mainly due to the works of Baues, Henn, Hennes, and the author, it has found new applications in algebraic topology, namely, in studying stable homotopy classes of polyhedra (see , [8], [4]-[7], ). In the survey the author has picked out the background of this approach, which is based on the trianguled structure of thew stable homotopy category. In this paper we show that the same method can be used in general situation, when we construct subcategories of a triangulated category from simpler ones (see Section 1). Then we summarize what can be done using this technique for

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