Lie algebras and Lie groups over noncommutative rings

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The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra $\gg$ sitting inside an associative algebra $A$ and any associative algebra $\FF$ we introduce and study the algebra $(\gg,A)(\FF)$, which is the Lie subalgebra of $\FF \otimes A$ generated by $\FF \otimes \gg$. In many examples $A$ is the universal enveloping algebra of $\gg$. Our description of the algebra $(\gg,A)(\FF)$ has a striking resemblance to the commutator expansions of $\FF$ used by M. Kapranov in his approach to noncommutative geometry. To each algebra $(\gg, A)(\FF)$ we associate a ``noncommutative algebraic'' group which naturally acts on $(\gg,A)(\FF)$ by conjugations and conclude the paper with some examples of such groups.
Introduction is improved and some typos corrected. To appear in "Advances"

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Quantum Algebra, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/155079

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701399
 http://arxiv.org/abs/math/0701399

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arXiv