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On the representation dimension of smash products

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Abstract

Let A be a finite dimensional algebra graded by a finite group, and let \(\Gamma \) be the corresponding smash product. We prove that if A is separably graded, then the representation dimension of \(\Gamma \) is at least the Oppermann dimension of A plus two; if A is in addition self-injective, then the representation dimension of \(\Gamma \) is at least the dimension of the stable A-module category plus two.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of South China, Hengyang, 421001, Hunan, People’s Republic of China

    Lijing Zheng & Chonghui Huang

  2. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan, People’s Republic of China

    Qianhong Wan

Authors
  1. Lijing Zheng
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  2. Chonghui Huang
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  3. Qianhong Wan
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Corresponding author

Correspondence to Qianhong Wan.

Additional information

Communicated by Rafaé Abéamowicz.

This work is partly supported by Natural Science Foundation of China #11271119, #11201220 and by Hunan Provincial Natural Science Foundation of China (#14JJ3099, #2016JJ6124, #2016JJ6049).

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Zheng, L., Huang, C. & Wan, Q. On the representation dimension of smash products. Adv. Appl. Clifford Algebras 27, 2885–2897 (2017). https://doi.org/10.1007/s00006-017-0783-1

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  • DOI: https://doi.org/10.1007/s00006-017-0783-1

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