Igor Burban
University of Paderborn
68 Papers
415 Citations
Igor Burban is an academic researcher from University of Paderborn. The author has contributed to research in topics: Indecomposable module & Derived category. The author has an hindex of 18, co-authored 65 publications. Previous affiliations of Igor Burban include Max Planck Society & University of Bonn.
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Papers
On the Hall algebra of an elliptic curve, I
Igor Burban,Olivier Schiffmann +1 more
TL;DR: In this article, the authors describe the Hall algebra H_X of an elliptic curve X defined over a finite field and show that the group SL(2,Z) of exact auto-equivalences of the derived category D^b(Coh(X)) acts on the Drinfeld double DH_X by algebra automorphisms.
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Cluster tilting for one-dimensional hypersurface singularities
TL;DR: In this paper, Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory were studied.
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Derived categories of nodal algebras
Igor Burban,Yuriy Drozd +1 more
TL;DR: In this paper, the authors classify indecomposable objects of the derived categories of finitely generated modules over certain infinite-dimensional algebras, which they call nodal algesbras and prove the Krull-Schmidt theorem for homotopy categories.
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Derived Categories of Nodal Algebras
Igor Burban,Yuriy Drozd +1 more
Abstract: In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known algebras as the complete ring of a double nodal point $\kk[[x,y]]/(xy)$ and the completed path algebra of the Gelfand quiver. As a corollary we obtain a description of the derived category of Harish-Chandra modules over $SL_{2}({\mathbb R})$. We also give an algorithm, which allows to construct projective resolutions of indecomposable complexes. In the appendix we prove the Krull-Schmidt theorem for homotopy categories.
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Coherent sheaves on rational curves with simple double points and transversal intersections
Igor Burban,Yurij Drozd +1 more
TL;DR: In this paper, the authors derived categories of coherent sheaves on some singular projective curves and gave a complete description of indecomposable objects using the technique of matrix problems.