A note on deformations of Gorenstein-projective modules over finite dimensional algebras

José A. Vélez-Marulanda

doi:10.15446/recolma.v53nsupl.84097

Publicado

2019-12-11

A note on deformations of Gorenstein-projective modules over finite dimensional algebras

Una nota acerca de deformaciones de módulos Gorenstein-proyectivos sobre álgebras de dimensión finita

DOI:

https://doi.org/10.15446/recolma.v53nsupl.84097

Palabras clave:

Deformations of modules, universal deformation rings, Gorenstein algebras, Gorenstein-projective modules (en)
Deformaciones de módulos, anillos universales de deformación, álgebras de Gorenstein, módulos Gorenstein-proyectivos (es)

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Autores/as

José A. Vélez-Marulanda Valdosta State University

Resumen (en)
Resumen (es)

In this note, we present a survey of results concerning universal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional algebras.

En esta nota, nosotros damos una revisión de resultados concernientes a anillos universales de deformación de módulos Gorenstein-proyectivos finitamente generados sobre álgebras de dimensión finita.

Referencias

M. Auslander and M. Brigder, Stable Module Theory, Memoirs of the American Mathematical Society, no. 94, American Mathematical Society, 1969.

M. Auslander and I. Reiten, Applications of contravariantly finite subcategories, Adv. in Math. 86 (1991), 111-152.

M. Auslander and I. Reiten, Cohen-Macaulay and Gorenstein Artin algebras, Representation Theory of Finite Groups and Finite-Dimensional Algebras (G. O. Michler and C. M. Ringel, eds.), Progress in Mathematics, no. 95, Birkhäuser Verlag Basel, 1991, pp. 221-245.

M. Auslander, I. Reiten, and S. Smalo, Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics, no. 36, Cambridge University Press, 1995.

V. Bekkert, H. Giraldo, and J. A. Vélez-Marulanda, Universal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional algebras, Submitted. Available in https://arxiv.org/abs/1705.05230.

D. J. Benson, Representations and Cohomology I: Basic representation theory of finite groups and associative algebras, Cambridge Studies in Advanced Mathematics 30, Cambridge University Press, 1991.

F. M. Bleher and S. N. Talbott, Universal deformation rings of modules for algebras of dihedral type of polynomial growth, Algebr. Represent. Theory 17 (2014), 289-303.

F. M. Bleher and J. A. Vélez-Marulanda, Universal deformation rings of modules over Frobenius algebras, J. Algebra 367 (2012), 176-202.

F. M. Bleher and J. A. Vélez-Marulanda, Deformations of complexes for finite dimensional algebras, J. Algebra 491 (2017), 90-140.

F. M. Bleher and D. J. Wackwitz, Universal deformation rings and self-injective Nakayama algebras, J. Pure Appl. Algebra 223 (2019), no. 1 218-244.

M. Broué, Equivalences of blocks of group algebras, Finite Dimensional Algebras and Related Topics (V. Dlab and L. L. Scott, eds.), NATO ASI Series, no. 424, Springer Netherlands, 1994, pp. 1-26.

X. Chen and M. Lu, Cohen-Macaulay Auslander algebras of skewed-gentle algebras, Comm. Algebra. 45 (2017), no. 2, 849-865.

X. W. Chen, Algebras with radical square zero are either self-injective or CM-free, Proc. Amer. Math. Soc. 140 (2012), no. 1, 93-98.

X. W. Chen, D. Shen, and G. Zhou, The Gorenstein-projective modules over a monomial algebra, Proc. Roy. Soc. Edinburgh Sect. A. 148 (2018), no. 6, 1115-1134.

X. W. Chen and L. G. Sun, Singular equivalences of Morita type, Preprint, 2012.

X. W. Chen and Y. Ye, Retractions and Gorenstein homological properties, Algebr. Represent. Theor. 17 (2014), 713-733.

E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), 611-633.

K. Erdmann, Blocks of Tame Representation Type and Related Algebras, Lectures Notes in Mathematics, no. 1428, Springer-Verlag, 1990.

Ch. GeiB and J. A. de la Peña, Auslander-Reiten components for clans, Bol. Soc. Mat. Mexicana 5 (1999), no. 3, 307-326.

T. Holm, Derived equivalence classication of algebras of dihedral, semidi-hedral, and quaternion type, J. Algebra 211 (1999), 159-205.

M. Kalck, Singularity categories of gentle algebras, Bull. London Math. Soc. 47 (2015), 65-74.

B. Mazur, An introduction to the deformation theory of Galois representations, Modular Forms and Fermat's Last Theorem (G. Cornell, J. H. Silverman, and G. Stevens, eds.), Springer-Verlag, Boston, MA, 1997, pp. 243-311.

J. Rickard, Derived categories as derived functors, J. London Math. Soc. 43 (1991), no. 2, 37-48.

C. M. Ringel, The Gorenstein projective modules for the Nakayama algebras. I, J. Algebra 385 (2013), 241-261.

M. Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222.

O. Skartsaeterhagen, Singular equivalence and the (Fg) condition, J. Algebra 452 (2016), 66-93.

A. Skowronski and K. Yamagata, Selfinjective algebras of quasitilted type, Trends in Representation Theory of Algebras and Related Topics (A. Skowronski, ed.), EMS Series of Congress Reports, European Mathematical Society, 2008, pp. 639-708.

A. Skowronski and K. Yamagata, Frobenius Algebras I: Basic Representation Theory, EMS Textbooks in Mathematics, vol. 12, European Mathematical Society, 2011.

J. A. Vélez-Marulanda, Universal deformation rings of strings modules over a certain symmetric special biserial algebra, Beitr. Algebra Geom. 56 (2015), no. 1, 129-146.

Z. Wang, Singular equivalence of Morita type with level, J. Algebra 439 (2015), 245-269.

C. A. Weibel, An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics, no. 38, Cambridge University Press, 1994.

A. Zaks, Injective dimensions of semi-primary rings, J. Algebra 13 (1969), 73-86.

G. Zhou and A. Zimmermann, On singular equivalences of Morita type, J. Algebra 385 (2013), 64-79.

Cómo citar

APA

Vélez-Marulanda, J. A. (2019). A note on deformations of Gorenstein-projective modules over finite dimensional algebras. Revista Colombiana de Matemáticas, 53(supl), 245–256. https://doi.org/10.15446/recolma.v53nsupl.84097

ACM

[1]

Vélez-Marulanda, J.A. 2019. A note on deformations of Gorenstein-projective modules over finite dimensional algebras. Revista Colombiana de Matemáticas. 53, supl (dic. 2019), 245–256. DOI:https://doi.org/10.15446/recolma.v53nsupl.84097.

ACS

(1)

Vélez-Marulanda, J. A. A note on deformations of Gorenstein-projective modules over finite dimensional algebras. rev.colomb.mat 2019, 53, 245-256.

ABNT

VÉLEZ-MARULANDA, J. A. A note on deformations of Gorenstein-projective modules over finite dimensional algebras. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. supl, p. 245–256, 2019. DOI: 10.15446/recolma.v53nsupl.84097. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/84097. Acesso em: 27 dic. 2025.

Chicago

Vélez-Marulanda, José A. 2019. «A note on deformations of Gorenstein-projective modules over finite dimensional algebras». Revista Colombiana De Matemáticas 53 (supl):245-56. https://doi.org/10.15446/recolma.v53nsupl.84097.

Harvard

Vélez-Marulanda, J. A. (2019) «A note on deformations of Gorenstein-projective modules over finite dimensional algebras», Revista Colombiana de Matemáticas, 53(supl), pp. 245–256. doi: 10.15446/recolma.v53nsupl.84097.

IEEE

[1]

J. A. Vélez-Marulanda, «A note on deformations of Gorenstein-projective modules over finite dimensional algebras», rev.colomb.mat, vol. 53, n.º supl, pp. 245–256, dic. 2019.

MLA

Vélez-Marulanda, J. A. «A note on deformations of Gorenstein-projective modules over finite dimensional algebras». Revista Colombiana de Matemáticas, vol. 53, n.º supl, diciembre de 2019, pp. 245-56, doi:10.15446/recolma.v53nsupl.84097.

Turabian

Vélez-Marulanda, José A. «A note on deformations of Gorenstein-projective modules over finite dimensional algebras». Revista Colombiana de Matemáticas 53, no. supl (diciembre 11, 2019): 245–256. Accedido diciembre 27, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/84097.

Vancouver

1.

Vélez-Marulanda JA. A note on deformations of Gorenstein-projective modules over finite dimensional algebras. rev.colomb.mat [Internet]. 11 de diciembre de 2019 [citado 27 de diciembre de 2025];53(supl):245-56. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/84097

Descargar cita

CrossRef Cited-by

3

1. José A. Vélez-Marulanda. (2021). On deformations of Gorenstein-projective modules over Nakayama and triangular matrix algebras. Journal of Pure and Applied Algebra, 225(4), p.106562. https://doi.org/10.1016/j.jpaa.2020.106562.

2. Jhony F. Caranguay-Mainguez, Pedro Rizzo, José A. Vélez-Marulanda. (2025). On universal deformation rings and stable homogeneous tubes. Communications in Algebra, , p.1. https://doi.org/10.1080/00927872.2025.2598422.

3. José A. Vélez-Marulanda, Héctor Suárez. (2024). A short note on deformations of (strongly) Gorenstein-projective modules over the dual numbers. São Paulo Journal of Mathematical Sciences, 18(2), p.1692. https://doi.org/10.1007/s40863-024-00453-4.