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2007•Journal of Generalized Lie Theory and ApplicationsOpen access

A canonical semi-classical star product

Lucian M. Ionescu, Papa A. Sissokho

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Abstract

We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within the class of graphs without circuits, without assuming the Jacobi identity. The proof is based on the unique factorization property of graph insertions.

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What this paper is about

We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within the class of graphs without circuits, without assuming the Jacobi identity. The proof is based on the unique factorization property of graph insertions.

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Available abstract

We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within the class of graphs without circuits, without assuming the Jacobi identity. The proof is based on the unique factorization property of graph insertions.

Key concepts: Star product, Mathematics, Star (game theory), Product (mathematics), Pure mathematics, Algebra over a field, Combinatorics, Mathematical physics

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