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- W2952318306 abstract "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." @default.
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- W2952318306 date "2007-01-15" @default.
- W2952318306 modified "2023-09-27" @default.
- W2952318306 title "Lie algebras and Lie groups over noncommutative rings" @default.
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