Abstract
Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group. There is a quiver QG with relations ρG such that the skew group algebras A[G] is Morita equivalent to the quotient algebra of path algebra kQG modulo ideal (ρG). Generally, the quiver QG is not connected. In this paper we develop a method to determine the number of connect components of QG. Meanwhile, we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.
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The authors would like to thank the referees for their helpful comments.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11871404, 11971398 and 12131018)
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Chen, J.M., Dong, Q. & Lin, Y.N. On Connected Components of Skew Group Algebras. Acta. Math. Sin.-English Ser. 39, 799–813 (2023). https://doi.org/10.1007/s10114-022-1237-9
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DOI: https://doi.org/10.1007/s10114-022-1237-9