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Noncommutative loops over Lie algebras and Lie groups

Retakh, V (Rutgers)
Thursday 21 December 2006, 11:30-12:30

Seminar Room 1, Newton Institute



In this talk I will introduce noncommutative loops over Lie algebras as a tool for studying algebraic groups over noncommutative rings.

Given a Lie algebra $g$ sitting inside an associative algebra $A$ and any associative algebra $F$, the $F$-loop algebra is the Lie subalgebra of tensor product $F\otimes A$ generated by $F \otimes g$.

For a large class of Lie algebras $g$, including semisimple ones, an explicit description of all $F$-loop algebras will be presented. This description has a striking resemblance to the commutator expansions of $F$ used by M. Kapranov in his approach to noncommutative geometry.

I will also define and study Lie groups associated with $F$-loop algebras.

This is a joint paper with A. Berenstein (Univ. of Oregon).

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