Homological invariants of generalized bound path algebras

Year 2026, Volume: 39 Issue: 39 , 50 - 66 , 10.01.2026

Viktor Chust Flavio U. Coelho

https://doi.org/10.24330/ieja.1707407

Cited By: 1

https://izlik.org/JA89CY23CX

Abstract

We study homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions for those algebras to be shod or quasitilted.

Keywords

Generalized path algebra , representation of generalized path algebras , homological dimension

References

• I. Assem and F. U. Coelho, Basic Representation Theory of Algebras, Graduate Texts in Mathematics, 283, Springer, Switzerland, 2020.
• I. Assem and F. U. Coelho, An Introduction to Module Theory, Oxford Graduate Text in Mathematics, 32, Oxford University Press, England, 2024.
• M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, England, 1995.
• A. B. Buan and Y. Zhou, Silted algebras, Adv. Math., 303 (2016), 859-887.
• V. Chust and F. U. Coelho, On the correspondence between path algebras and generalized path algebras, Comm. Algebra, 50(5) (2022), 2056-2071.
• V. Chust and F. U. Coelho, Representations of generalized bound path algebras, Sao Paulo J. Math. Sci., 17(2) (2023), 483-504.
• F. U. Coelho and M. Lanzilotta, Algebras with small homological dimensions, Manuscripta Math., 100(1) (1999), 1-11.
• F. U. Coelho and S. X. Liu, Generalized path algebras, in: Interaction between ring theory and representations of algebras, Proceedings of the conference held in Murcia, Spain, Lecture Notes in Pure and Appl. Math., Dekker, New York, 210 (2000), 53-66.
• C. Geiss, B. Leclerc and J. Schröer, Quivers with relations for symmetrizable Cartan matrices I: Foundations, Invent. Math., 209(1) (2017), 61-158.
• D. Happel, I. Reiten and S. O. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc., 120 (1996), 575 (88 pp).
• M. Hazewinkel, N. Gubareni and V. V. Kirichenko, Algebras, Rings and Modules, 2, Mathematics and its Applications, 586, Springer, 2007.
• R. M. Ibanez-Cobos, G. Navarro and J. Lopez-Pena, A note on generalized path algebras, Rev. Roumaine Math. Pures Appl., 53(1) (2008), 25-36.
• J. Külshammer, Pro-species of algebras I: basic properties, Algebr. Represent. Theory, 20(5) (2017), 1215-1238.
• F. Li, Characterization of left artinian algebras through pseudo path algebras, J. Aust. Math. Soc., 83(3) (2007), 385-416.
• F. Li, Modulation and natural valued quiver of an algebra, Pacific J. Math., 256(1) (2012), 105-128.