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Abstract:

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.

Registro:

Documento: Artículo
Título:Isomorphisms of Nonnoetherian Down-Up Algebras
Autor:Chouhy, S.; Solotar, A.
Filiación:IMAS, UBA-CONICET, Consejo Nacional de Investigaciones Cientícas y Técnicas, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Down-up algebra; Isomorphism; Monomial; Nonnoetherian; Set theory; Functors; Isomorphism; Isomorphism problems; Monomial; Non-commutative; Nonnoetherian; Polynomial algebra; Weyl algebra; Algebra
Año:2018
Volumen:21
Número:6
Página de inicio:1343
Página de fin:1352
DOI: http://dx.doi.org/10.1007/s10468-017-9749-1
Título revista:Algebras and Representation Theory
Título revista abreviado:Algebr Represent Theory
ISSN:1386923X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v21_n6_p1343_Chouhy

Referencias:

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Citas:

---------- APA ----------
Chouhy, S. & Solotar, A. (2018) . Isomorphisms of Nonnoetherian Down-Up Algebras. Algebras and Representation Theory, 21(6), 1343-1352.
http://dx.doi.org/10.1007/s10468-017-9749-1
---------- CHICAGO ----------
Chouhy, S., Solotar, A. "Isomorphisms of Nonnoetherian Down-Up Algebras" . Algebras and Representation Theory 21, no. 6 (2018) : 1343-1352.
http://dx.doi.org/10.1007/s10468-017-9749-1
---------- MLA ----------
Chouhy, S., Solotar, A. "Isomorphisms of Nonnoetherian Down-Up Algebras" . Algebras and Representation Theory, vol. 21, no. 6, 2018, pp. 1343-1352.
http://dx.doi.org/10.1007/s10468-017-9749-1
---------- VANCOUVER ----------
Chouhy, S., Solotar, A. Isomorphisms of Nonnoetherian Down-Up Algebras. Algebr Represent Theory. 2018;21(6):1343-1352.
http://dx.doi.org/10.1007/s10468-017-9749-1