Pre-Lie Deformation Theory
نویسندگان
چکیده
منابع مشابه
Arithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
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This is an expository paper written in 1999 and published in Seminari di Geometria Algebrica 1998-1999, Scuola Normale Superiore (1999). Six years later some arguments used here appear quite naive and obsolete but, in view of the several citations that this paper has obtained in the meantime, I preferred don’t change the mathematical contents and to fix only some typos and minor mistakes. For a...
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Deformation Theory is a natural generalization of Lie Theory, from Lie groups and their linearization, Lie algebras, to differential graded Lie algebras and their higher order deformations, quantum groups. The article focuses on two basic constructions of deformation theory: the universal solution of Maurer-Cartan Equation (MCE), which plays the role of the exponential of Lie Theory, and its in...
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In the last decade the interest in deformation theory has grown in many areas of mathematics and physics. The deformation question is completely solved by describing a ‘‘versal’’ deformation of the given object; such a deformation induces all the other deformations. This problem turns out to be hard and a general procedure for solving this was given only recently in FF2 for Lie algebras. It is ...
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We find a one parameter family of quadratic Poisson structures on R 4 × SL(2, C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz group, as well as b) that it reduces to the standard Poincaré algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer t...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2016
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2016-16-3-505-543