# Meeting Details

Title: Lie algebras and Lie groups over noncommutative rings Algebra and Number Theory Seminar Vladimir Retakh, Rutgers University For any Lie algebra $g$ sitting inside an associative algebra $A$ and any associative algebra $R$ we introduce and study Lie algebra $(g,A)(R)$ as the Lie subalgebra  of $R otimes A$ generated by $R otimes g$. In many examples $A$ is the universal enveloping algebra of $g$. Our description of algebra $(gg ,A)(R)$ has a striking resemblance to the commutator expansions of $R$ used by M. Kapranov in his approach to noncommutative algebraic geometry. To each Lie algebra $(g, A)(R)$ we associate a noncommutative algebraic''group which naturally acts on $(g, A)(R)$ by conjugations and conclude with some examples of such groups. (joint with A. Berenstein from U. of Oregon)