Degeneration of A-infinity modules

Bernt Tore Jensen; Dag Madsen; Xiuping Su

doi:10.1090/S0002-9947-09-04693-5

Degeneration of A-infinity modules

Bernt Tore Jensen, Dag Madsen, Xiuping Su

Department of Mathematical Sciences

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Abstract

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedtmann for modules.

Original language	English
Pages (from-to)	4125-4142
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	8
Early online date	23 Feb 2009
DOIs	https://doi.org/10.1090/S0002-9947-09-04693-5
Publication status	Published - Aug 2009

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First published in Transactions of the American Mathematical Society, 361 (8), published by the American Mathematical Society

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title = "Degeneration of A-infinity modules",

abstract = "In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedtmann for modules.",

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AB - In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedtmann for modules.

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Degeneration of A-infinity modules

Abstract

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