2020/10/07 by Jin Yun Guo, Cong Xiao, Guo, Jin Yun +3
Mathematics · #16G20 #16G60 #16S35 #20C05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2010.03100
openalex publication_date 2020/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, \mathbb 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, \mathbb C) and of the finite subgroups obtained from embedding SL(2, \mathbb C) into SL(3,\mathbb C).