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2021, Volume 29, Issue 4: 2687-2718. doi: 10.3934/era.2021009
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On n-slice algebras and related algebras

  • LCSM(Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China
  • Received: 01 April 2020 Revised: 01 December 2020 Published: 01 September 2021

  • Primary: 16G20, 16G60, 16S35; Secondary: 20C05

  • The n-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of n-slice algebras via their (n+1)-preprojective algebras and the trivial extensions of their quadratic duals. One can always relate tame n-slice algebras to the McKay quiver of a finite subgroup of GL(n+1,C). In the case of n=2, we describe the relations for the 2-slice algebras related to the McKay quiver of finite Abelian subgroups of SL(3,C) and of the finite subgroups obtained from embedding SL(2,C) into SL(3,C).

    Citation: Jin-Yun Guo, Cong Xiao, Xiaojian Lu. On n-slice algebras and related algebras[J]. Electronic Research Archive, 2021, 29(4): 2687-2718. doi: 10.3934/era.2021009

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  • The n-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of n-slice algebras via their (n+1)-preprojective algebras and the trivial extensions of their quadratic duals. One can always relate tame n-slice algebras to the McKay quiver of a finite subgroup of GL(n+1,C). In the case of n=2, we describe the relations for the 2-slice algebras related to the McKay quiver of finite Abelian subgroups of SL(3,C) and of the finite subgroups obtained from embedding SL(2,C) into SL(3,C).




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