The Ribbon Elements of the Quantum Double of Generalized Taft–Hopf Algebra

Hua Sun, Yuyan Zhang (), Ziliang Jiang, Mingyu Huang and Jiawei Hu
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Hua Sun: College of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Yuyan Zhang: College of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Ziliang Jiang: College of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Mingyu Huang: College of Mathematical Science, Yangzhou University, Yangzhou 225002, China
Jiawei Hu: College of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Mathematics, 2024, vol. 12, issue 12, 1-12

Abstract: Let s , t be two positive integers and k be an algebraically closed field with char ( k ) ∤ s t . We show that the Drinfeld double D ( ⋀ s t , t * c o p ) of generalized Taft–Hopf algebra ⋀ s t , t * c o p has ribbon elements if and only if t is odd. Moreover, if s is even and t is odd, then D ( ⋀ s t , t * c o p ) has two ribbon elements, and if both s and t are odd, then D ( ⋀ s t , t * c o p ) has only one ribbon element. Finally, we compute explicitly all ribbon elements of D ( ⋀ s t , t * c o p ) .

Keywords: quantum double; ribbon Hopf algebra; quasi-triangular Hopf algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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