### Recovering automorphisms of quantum spaces

## Abstract

It has long been expected, and is now proved in many important cases,

that quantum algebras are more rigid than their classical limits. That is, they

have much smaller automorphism groups. This begs the question of whether this

broken symmetry can be recovered.

I will outline an approach to this question using the ideas of noncommutative

projective geometry, from which we see that the correct object to study is a

groupoid, rather than a group, and maps in this groupoid are the replacement

for automorphisms. I will illustrate this with the example of quantum

projective space.

This is joint work with Nicholas Cooney (Clermont-Ferrand).