The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra
Hua Sun, Yuyan Zhang, Libin Li

TL;DR
This paper characterizes when the Drinfeld double of Radford's Hopf algebra has ribbon elements, showing it depends on the parity of the integer parameters, and explicitly computes these ribbon elements.
Contribution
It provides a complete characterization of the existence and number of ribbon elements in the Drinfeld double of Radford Hopf algebras, including explicit computations.
Findings
Ribbon elements exist if and only if n is odd.
Number of ribbon elements depends on the parity of m and n.
Explicit formulas for all ribbon elements are provided.
Abstract
Let , be two positive integers, be an algebraically closed field with char(. Radford constructed an -dimensional Hopf algebra such that its Jacobson radical is not a Hopf ideal. We show that the Drinfeld double of Radford Hopf algebra has ribbon elements if and only if is odd. Moreover, if is even and is odd, then has two ribbon elements, if both and are odd, then has only one ribbon element. Finally, we compute explicitly all ribbon elements of .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Logic
