|Location:||MSRI: Simons Auditorium|
We will describe a general rigidity theorem for quantum tori.
It leads to a scheme that can be used to classify the (full) automorphism groups of algebras that admit one quantum cluster (i.e. can be squeezed between a quantum affine space algebra and the corresponding quantum torus).
The technique has a broad range of applications and in particular settles a couple of conjectures of Andruskiewitsch-Dumas and Launois-Lenagan. The former describes the automorphism groups of the algebras U_q^+(g) and the latter those of the algebras of square quantum matrices.