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The octonions form an Azumaya algebra in certain braided linear Gr-categories

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Abstract

By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the octonions form an Azumaya algebra in some suitable braided linear Gr-categories.

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Authors and Affiliations

  1. School of Mathematical Science, Shandong Normal University, Jinan, 250014, China

    Tao Cheng

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Hua-Lin Huang & Yuping Yang

  3. Department WNI, University of Hasselt, Universitaire Campus, 3590, Diepenbeek, Belgium

    Yinhuo Zhang

Authors
  1. Tao Cheng
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  2. Hua-Lin Huang
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  3. Yuping Yang
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  4. Yinhuo Zhang
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Corresponding author

Correspondence to Hua-Lin Huang.

Additional information

Supported by SRFDP 20130131110001, SDNSF ZR2013AM022, NSFC 11471186 and 11571199.

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Cheng, T., Huang, HL., Yang, Y. et al. The octonions form an Azumaya algebra in certain braided linear Gr-categories. Adv. Appl. Clifford Algebras 27, 1055–1064 (2017). https://doi.org/10.1007/s00006-016-0656-z

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  • DOI: https://doi.org/10.1007/s00006-016-0656-z

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