Quantum Groups Seminar

The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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Speaker: Alexandru Chirvasitu (University at Buffalo).

Title: Non-commutative balls and quantum group structures.

AbstractThe Toeplitz algebra attached to the unit disk is the universal C*-algebra generated by an isometry, and is a non-commutative analogue of the unit disk. Similarly, one can attach algebras to non-commutative counterparts of non-compact Hermitian symmetric spaces. I will discuss results to the effect that such quantum spaces cannot admit quantum group structures, i.e. their attached non-commutative “function algebras” do not admit reasonable Hopf algebra structures.

(joint w/ Jacek Krajczok and Piotr Soltan)