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Phase Spaces and Deformation Theory

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Abstract

In the papers (Laudal in Contemporary Mathematics, vol. 391, [2005]; Geometry of time-spaces, Report No. 03, [2006/2007]), we introduced the notion of (non-commutative) phase algebras (spaces) Ph n(A), n=0,1,…,∞ associated to any associative algebra A (space), defined over a field k. The purpose of this paper is to study this construction in some more detail. This seems to give us a possible framework for the study of non-commutative partial differential equations. We refer to the paper (Laudal in Phase spaces and deformation theory, Report No. 09, [2006/2007]), for the applications to non-commutative deformation theory, Massey products and for the construction of the versal family of families of modules. See also (Laudal in Homology, Homotopy, Appl. 4:357–396, [2002]; Proceedings of NATO Advanced Research Workshop, Computational Commutative and Non-Commutative Algebraic Geometry, [2004]).

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  1. Institute of Mathematics, University of Oslo, Box.1053, Blindern, 0316, Oslo, Norway

    Olav Arnfinn Laudal

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  1. Olav Arnfinn Laudal
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Correspondence to Olav Arnfinn Laudal.

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Laudal, O.A. Phase Spaces and Deformation Theory. Acta Appl Math 101, 191–204 (2008). https://doi.org/10.1007/s10440-008-9192-8

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  • DOI: https://doi.org/10.1007/s10440-008-9192-8

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