Resumen de Rigidity of quantum tori and the Andruskiewitsch–Dumas conjecture

Milen Yakimov

• We prove the Andruskiewitsch–Dumas conjecture that the automorphism group of the positive part of the quantized universal enveloping algebra Uq(g)Uq(g) of an arbitrary finite dimensional simple Lie algebra gg is isomorphic to the semidirect product of the automorphism group of the Dynkin diagram of gg and a torus of rank equal to the rank of gg . The key step in our proof is a rigidity theorem for quantum tori. It has a broad range of applications. It allows one to control the (full) automorphism groups of large classes of associative algebras, for instance quantum cluster algebras.