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Survey of Quantum Symmetry in the context of Hopf (co)actions

Banff International Research Station for Mathematical Innovation and Discovery

Quantum objects and their noncommutative algebras of functions have been ubitiquous in mathematics and physics– thus, an appropriate notion of symmetry is needed. As explained by Drinfel′d in his 1986 ICM address, replacing group actions with actions of Hopf algebras is an effective approach. For instance, one can deform group actions on classical objects (resp. commutative function algebras) to obtain (co)actions of Hopf algebras on quantum objects (resp. noncommutative function algebras). But this certainly does not account for all instances of Quantum Symmetry. In this talk, I will provide a survey of recent results on Hopf (co)actions on algebras. Classification results, including some from the analytic context, and many examples will be included.

Mathematics; Category theory; homological algebra; Quantum theory; Algebraic structures

video/mp4

Author affiliation: Temple University

2017-02-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60601

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/