Isomorphisms of Nonnoetherian Down-Up Algebras
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 A1 for nonzero γ....
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_1386923X_v21_n6_p1343_Chouhy |
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todo:paper_1386923X_v21_n6_p1343_Chouhy2023-10-03T16:12:23Z Isomorphisms of Nonnoetherian Down-Up Algebras Chouhy, S. Solotar, A. Down-up algebra Isomorphism Monomial Nonnoetherian Set theory Functors Isomorphism Isomorphism problems Monomial Non-commutative Nonnoetherian Polynomial algebra Weyl algebra Algebra 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 A1 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. © 2017, Springer Science+Business Media B.V., part of Springer Nature. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1386923X_v21_n6_p1343_Chouhy |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Down-up algebra Isomorphism Monomial Nonnoetherian Set theory Functors Isomorphism Isomorphism problems Monomial Non-commutative Nonnoetherian Polynomial algebra Weyl algebra Algebra |
| spellingShingle |
Down-up algebra Isomorphism Monomial Nonnoetherian Set theory Functors Isomorphism Isomorphism problems Monomial Non-commutative Nonnoetherian Polynomial algebra Weyl algebra Algebra Chouhy, S. Solotar, A. Isomorphisms of Nonnoetherian Down-Up Algebras |
| topic_facet |
Down-up algebra Isomorphism Monomial Nonnoetherian Set theory Functors Isomorphism Isomorphism problems Monomial Non-commutative Nonnoetherian Polynomial algebra Weyl algebra Algebra |
| description |
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 A1 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. © 2017, Springer Science+Business Media B.V., part of Springer Nature. |
| format |
JOUR |
| author |
Chouhy, S. Solotar, A. |
| author_facet |
Chouhy, S. Solotar, A. |
| author_sort |
Chouhy, S. |
| title |
Isomorphisms of Nonnoetherian Down-Up Algebras |
| title_short |
Isomorphisms of Nonnoetherian Down-Up Algebras |
| title_full |
Isomorphisms of Nonnoetherian Down-Up Algebras |
| title_fullStr |
Isomorphisms of Nonnoetherian Down-Up Algebras |
| title_full_unstemmed |
Isomorphisms of Nonnoetherian Down-Up Algebras |
| title_sort |
isomorphisms of nonnoetherian down-up algebras |
| url |
http://hdl.handle.net/20.500.12110/paper_1386923X_v21_n6_p1343_Chouhy |
| work_keys_str_mv |
AT chouhys isomorphismsofnonnoetheriandownupalgebras AT solotara isomorphismsofnonnoetheriandownupalgebras |
| _version_ |
1782024030861131776 |