Hopf algebras and duality

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• Astrid Jahn (University of Glasgow)
• Friday 16 March 2012, 14:00-15:00
• MR13.

If you have a question about this talk, please contact Jonathan Nelson.

Hopf algebras are a type of algebra whose structure naturally gives them a great deal of symmetry. One of the consequences of this is that in the finite-dimensional case, the dual of a Hopf algebra also has a canonical Hopf algebra structure. In the infinite-dimensional case this breaks down, and a subalgebra of the dual called the finite dual is usually considered instead. However, examples show that the finite dual lacks many of the properties we would like it to satisfy. I look at whether there is a better alternative for the specific class of Hopf algebras I am interested in, namely those satisfying the Artin-Schelter Gorenstein condition. I also look at some of the known results in the finite-dimensional case that involve the dual, particularly Radford’s formula for the fourth power of the antipode, and possible extensions to infinite-dimensional Hopf algebras.

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

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