Phase Spaces and Deformation Theory |
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Authors: | Olav Arnfinn Laudal |
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Affiliation: | (1) Institute of Mathematics, University of Oslo, Box.1053, Blindern, 0316 Oslo, Norway |
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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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Keywords: | Associative algebra Modules Simple modules Extensions Deformation theory Moduli spaces Non-commutative algebraic geometry Time Relativity theory Quantum theory |
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