Cluster-tilted and quasi-tilted algebras

Ibrahim Assem; Ralf Schiffler; Khrystyna Serhiyenko

doi:10.1016/j.jpaa.2016.12.008

Cluster-tilted and quasi-tilted algebras

Ibrahim Assem
, Ralf Schiffler
, Khrystyna Serhiyenko

Mathematics

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi–Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type.

Idioma original	English
Páginas (desde-hasta)	2266-2288
Número de páginas	23
Publicación	Journal of Pure and Applied Algebra
Volumen	221
N.º	9
DOI	https://doi.org/10.1016/j.jpaa.2016.12.008
Estado	Published - sept 1 2017

Nota bibliográfica

Publisher Copyright:
© 2016 Elsevier B.V.

Financiación

The first author gratefully acknowledges partial support from the NSERC of Canada. The second author was supported by the NSF CAREER grant DMS-1254567 and by the University of Connecticut. The third author was supported by the NSF Postdoctoral fellowship MSPRF-1502881.

Financiadores	Número del financiador
NSERC of Canada University
Connecticut 06520 Yale University New Haven Connecticut 06520	MSPRF-1502881
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	1254567, 1502881

ASJC Scopus subject areas

Algebra and Number Theory

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AU - Serhiyenko, Khrystyna

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AB - In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi–Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type.

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Cluster-tilted and quasi-tilted algebras

Resumen

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Financiación

ASJC Scopus subject areas

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