Paula Carvalho (Porto), The automorphism group and the skew field of fractions of Noetherian Down-Up algebras.

Abstract:

Down-Up algebras were introduced by G. Benkart and T. Roby in 1998. They are associative algebras generated by two generators satisfying two relations depending on three parameters. In the first part of the talk we will revise some properties of these algebras and describe the automorphism group of some Noetherian Down-Up algebras. This work is based on a paper with Samuel Lopes where the automorphism group of a larger class of algebras is studied. In the second part of the talk the rational equivalence of these algebras is discussed.