Quantum symmetries of noncommutative algebras

A Royal Irish Academy invited lecture by Professor Christian Lomp (Porto University, Portugal)

Quantum symmetries of noncommutative algebras

Symmetries of a space can be described by group actions, which in turn can be realised as group actions on the algebra of functions on that space. Actions of Hopf algebras on noncommutative algebras are viewed as “quantum” analogues of such symmetries, where the algebras represent functions on a “noncommutative” space. Classical results in representation theory ensure that group representations decompose into irreducibles; Hopf algebras with this property are called semisimple. In 2014, Etingof and Walton showed that if a semisimple Hopf algebra acts on a commutative integral domain, the action must factor through a group — implying that no genuine “quantum symmetry” exists for commutative domains. In this talk, Professor Christian Lomp (Porto University, Portugal) will present a new construction of semisimple Hopf algebras that yields genuine quantum symmetries of noncommutative domains.

The Synge Lecture Theatre is located within the Hamilton Building at Trinity College Dublin, which is situated at the east end of the campus near Westland Row.

The postcode for this location is: Dublin 2, D02 PN40, Ireland

Image transcript

Event & header page image 

Cover of a book titled Mathematical processing featuring abstract mathematical symbols and a modern design.

Access requirements

Have you got any access requirements that we can assist you with, so that you can fully engage with our event? Please let us know by contacting our access officer in advance of the event, by email: accessofficer@ria.ie