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On n-cubic Pyramid Algebras

Authors
  • Guo, Jin Yun1
  • Luo, Deren2
  • 1 Hunan Normal University, Department of Mathematics and Key Laboratory of HPCSIP (Ministry of Education of China), Changsha, China , Changsha (China)
  • 2 Hunan Normal University, Department of Mathematics, Changsha, China , Changsha (China)
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
Mar 28, 2016
Volume
19
Issue
4
Pages
991–1016
Identifiers
DOI: 10.1007/s10468-016-9608-5
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this paper we study a class of algebras having n-dimensional pyramid shaped quiver with n-cubic cells, which we called n-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic n-Auslander absolutely n-complete algebras introduced by Iyama. We show that the projective resolutions of the simples of n-cubic pyramid algebras can be characterized by n-cuboids, and prove that they are periodic. So these algebras are almost Koszul and (n−1)-translation algebras. We also recover Iyama’s cone construction for n-Auslander absolutely n-complete algebras using n-cubic pyramid algebras and the theory of n-translation algebras.

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