Covering functors without groups

JOURNAL OF ALGEBRA

卷:321

Article

de la Pena, Jose A.²  Julia Redondo, Maria¹ 

[1] Univ Nacl Sur, Dept Matemat, RA-8000 Bahia Blanca, Buenos Aires, Argentina

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

关键词: Coverings;    Representation type;   

DOI  :  10.1016/j.jalgebra.2009.02.023

来源: Elsevier

【 摘 要 】

Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtnnann, Algebren, Darstellungskocher, Uberlagerungen und zuruch, Comment. Math. HeIv. 55 (1980) 199-224] and later for finite-dimensional algebras in [K. Bongartz, R Gabriel, Covering spaces in representation theory, Invent. Math. 65 (3) (1982) 331378; P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. Representation Theory 1, Puebla, 1980, in: Lecture Notes in Math., vol. 903, Springer, 1981. pp. 68-105; R. Martinez-Villa, J.A. de la Pefia, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (3) (1983) 277-292]. The best understood class of covering functors is that of Galois covering functors F : A -> B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Calais class and for which classical Galois covering-type results still hold. For instance, if F : A 6 is a balanced covering functor, where A and B are linear categories over an algebraically closed field. and B is tame, then A is tame. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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