Isomorphisms of non noetherian down-up algebras

ANDREA SOLOTAR; SERGIO CHOUHY

Algebras and Representation Theory

SPRINGER

Lugar: Berlin; Año: 2018 vol. 21 p. 1343 - 1352

1386-923X

We solve the isomorphism problem for non noetherian down-up algebrasA(α, 0, γ) by lifting isomorphisms between some of their non commutativequotients. The quotients we consider are either quantum polynomial algebrasin two variables for γ = 0 or quantum versions of the Weyl algebra A_1 for nonzero γ. In particular we obtain that no other down-up algebra is isomorphic tothe monomial algebra A(0, 0, 0). We prove in the second part of the article thatthis is the only monomial algebra within the family of down-up algebras. Ourmethod uses homological invariants that determine the shape of the possiblequivers and we apply the abelianization functor to complete the proof.https://doi.org/10.1007/s10468-017-9749-1