Algebras and Representation Theory

, Volume 21, Issue 6, pp 1343–1352 | Cite as

Isomorphisms of Nonnoetherian Down-Up Algebras

  • Sergio Chouhy
  • Andrea Solotar


We solve the isomorphism problem for nonnoetherian down-up algebras A(α, 0, γ) by lifting isomorphisms between some of their noncommutative quotients. The quotients we consider are either quantum polynomial algebras in 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 to the monomial algebra A(0, 0, 0). We prove in the second part of the article that this is the only monomial algebra within the family of down-up algebras. Our method uses homological invariants that determine the shape of the possible quivers and we apply the abelianization functor to complete the proof.


Down-up algebra Isomorphism Nonnoetherian Monomial 

Mathematics Subject Classification (2010)

16D70 16E05 


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.IMAS, UBA-CONICET, Consejo Nacional de Investigaciones Cientícas y TécnicasCiudad Universitaria, Pabellón IBuenos AiresArgentina
  2. 2.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires, Ciudad UniversitariaBuenos AiresArgentina

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