The Crossed Product of Finite Hopf C *-Algebra and C *-Algebra

Xiaomin Wei, Lining Jiang and Dianlu Tian
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Xiaomin Wei: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Lining Jiang: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Dianlu Tian: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2021, vol. 9, issue 9, 1-9

Abstract: Let H be a finite Hopf C * -algebra and A a C * -algebra of finite dimension. In this paper, we focus on the crossed product A ? H arising from the action of H on A , which is a ?-algebra. In terms of the faithful positive Haar measure on a finite Hopf C * -algebra, one can construct a linear functional on the ?-algebra A ? H , which is further a faithful positive linear functional. Here, the complete positivity of a positive linear functional plays a vital role in the argument. At last, we conclude that the crossed product A ? H is a C * -algebra of finite dimension according to a faithful ?- representation.

Keywords: Hopf C *-algebra; module algebra; crossed product; completely positive linear map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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