A Duality Theorem for Hopf Quasimodule Algebras

Huaiwen Guo and Shuanhong Wang ()
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Huaiwen Guo: School of Mathematics, Southeast University, Nanjing 210096, China
Shuanhong Wang: Shing-Tung Yau Center, School of Mathematics, Southeast University, Nanjing 210096, China

Mathematics, 2023, vol. 11, issue 6, 1-16

Abstract: In this paper, we introduce and study two smash products A ★ H for a left H -quasimodule algebra A over a Hopf quasigroup H over a field K and B # U for a coquasi U -module algebra B over a Hopf coquasigroup U , respectively. Then, we prove our duality theorem ( A ★ H ) # H * ≅ A ⊗ ( H # H * ) ≅ A ⊗ M n ( K ) ≅ M n ( A ) in the setting of a Hopf quasigroup H of dimension n . As an application of our result, we consider a special case of a finite quasigroup.

Keywords: quasigrups; Hopf (co)quasigroups; duality theorem; quasimodule algebras; coquasi module algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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