For more information about this meeting, contact Robert Vaughan.
| Title: | Lie algebras and Lie groups over noncommutative rings |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Vladimir Retakh, Rutgers University |
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| Abstract: |
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| 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) |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 10 / 23 / 2008 |
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| Time: | 11:15am - 12:05pm |
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