Quantum symmetric algebras

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• Alex Shannon, University of Cambridge
• Friday 09 November 2012, 14:00-15:00
• MR4.

If you have a question about this talk, please contact Joanna Fawcett.

Given a representation V of a Lie algebra, the symmetric algebra S(V) is also a representation in a natural way. If one deforms the universal enveloping algebra of the Lie algebra as a Hopf algebra to obtain the corresponding quantum group, S(V) deforms to a representation of the quantum group, but in general this deformation fails to be a deformation of algebras. One can, however, emulate the construction of the symmetric algebra for representations of the quantum group, and this turns out to be a deformation of a subalgebra of S(V). The question we address in this talk is: how much smaller is this than S(V)?

This talk is part of the Junior Algebra and Number Theory seminar series.

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