Some remarks on Hom-modules and Hom-path algebras

Abstract

This paper deals with injective and projective right Hom-H-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that HomModH is an Abelian category. Next, the authors define Hom-path algebras and construct Hom-path algebras of some quivers.

Keywords

Hom-Module / Hom-Algebra / Quiver

References

[1] Makhlouf A, Silvestrov S. Hom-algebra structures. J. Gen. Lie Theory Appl., 2008, 2(2): 51-64

[2] Makhlouf A, Silvestrov S. Hom-algebras and Hom-coalgebras. J. Algebra Appl., 2010, 9: 553-589

[3] Yau D. Enveloping algebras of Hom-Lie algebras. J. Gen. Lie Theory Appl., 2008, 2(2): 95-108

[4] Yau D. Hom-algebras and homology. J. Lie Theory, 2009, 19: 409-421

[5] Yau D. Hom-bialgebras and comodule Hom-algebras. International Electronic Journal of Algebra, 2010, 8: 45-64

[6] Rotman J J. An Introduction to Homological Algebra, 2009 (2nd Edition) New York: Springer-Verlag

[7] Zhou B X. Homological Algebra, 1998, Beijing: Science Press

[8] Makhlouf A, Reiteni I, Smalφ S O. Representation Theory of Artin Algebras, 1995, Cambridge: Cambridge University Press

[9] Woodcock D. Some categorical remarks on the representation theory of coalgebras. Comm. Algebra, 1997, 25(9): 2775-2794

[10] Simson D. Path coalgebras of quiver with relations and a tame-wild dichotomy problem for coalgebras. Lecture Notes in Pure and Appl. Math., Marcel-Dekker, 2004, 236: 465-492

[11] Makhlouf, A., Paradigm of nonassociative Hom-algebras and Hom-superalgebras, arXiv:1001.4240v1.