An introduction to noncommutative deformations of modules

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dc.creatorEriksen, Eivind
dc.date2003-03-13
dc.date.accessioned2026-07-07T06:26:51Z
dc.date.available2026-07-07T06:26:51Z
dc.descriptionThis paper gives an elementary introduction to noncommutative deformations of modules. The main results of this deformation theory are due to Laudal. Let k be an algebraically closed (commutative) field, let A be an associative k-algebra, and let M = {M_1, ..., M_p} be a finite family of left A-modules. We study the simultaneous formal deformations of the family M, described by the noncommutative deformation functor Def(M): a(p) -> Sets introduced by Laudal. In particular, we prove that the deformation functor Def(M) has a pro-representing hull H(M), unique up to non-canonical isomorphism, and describe how to calculate H(M) using the Ext groups of the family M and their matric Massey products.
dc.description33 pages, AMS-LaTeX, uses package Xy-pic, submitted to Noncommutative Geometry and Rings (Almeria 2002) conference proceedings
dc.identifierhttps://arxiv.org/abs/math/0303166
dc.identifierhttp://arxiv.org/abs/math/0303166
dc.identifierNoncommutative Algebra and Geometry, (Corrado De Concini, Freddy Van Oystaeyen, Nikolai Vavilov, and Anatoly Yakovlev, eds.), Lecture Notes in Pure and Applied Mathematics, vol. 243, Chapman & Hall/CRC, 2005, pp. 90-126
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97237
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject14D15; 14B12
dc.titleAn introduction to noncommutative deformations of modules
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