Results 11 to 20 of about 133 (132)
Monadic cointegrals and applications to quasi-Hopf algebras [PDF]
Journal of Pure and Applied Algebra, 2021 For $\mathcal{C}$ a finite tensor category we consider four versions of the central monad, $A_1, \dots, A_4$ on $\mathcal{C}$. Two of them are Hopf monads, and for $\mathcal{C}$ pivotal, so are the remaining two. In that case all $A_i$ are isomorphic as Hopf monads. We define a monadic cointegral for $A_i$ to be an $A_i$-module morphism $\mathbf{1} \to
Berger, Johannes +2 more
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Induction and Coinduction for Hopf Algebras: Applications [PDF]
Journal of Algebra, 1994 Let \(H\) be a finite dimensional and semisimple Hopf algebra, and \(A\) an \(H\)-module algebra. The authors study the induced and coinduced functors from the ring of invariants of \(A\) and show, in analogy with Theorem 1.1 of \textit{C. Năstăsescu} [J. Algebra 120, 119-138 (1989; Zbl 0678.16001)] that they arise in adjoint pairs.
Caenepeel, S. +2 more
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The applications of probability groups on Hopf algebras [PDF]
Communications in Algebra, 2020 20pages
Zhou, Jingheng, Zhu, Shenglin
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An Application of Finite Groups to Hopf algebras
European Journal of Pure and Applied Mathematics, 2021 Kaplansky’s famous conjectures about generalizing results from groups to Hopf al-gebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in [8] and [10] have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results.
Tahani Al-Mutairi +1 more
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Fuzziness on Hopf Algebraic Structures with Its Application
Journal of New Theory, 2021 The objective of writing this manuscript is to apply the concept of fuzzy set on some basic Hopf algebraic structures. In this manuscript, the novel concepts of fuzzy Hopf subalgebra, fuzzy Hopf ideal, and fuzzy H-submodule are proposed. Some properties of these concepts are discussed, and some significant results are also proved in it.
Munir Ahmed +2 more
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Factorizable quasi-Hopf algebras—applications
Journal of Pure and Applied Algebra, 2004 We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double $D(H)$ of any finite dimensional quasi-Hopf algebra $H$ is factorizable, and we characterize $D(H)$ when $H$ itself is factorizable.
Bulacu, Daniel, Torrecillas, Blas
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Hopf subalgebras of pointed Hopf algebras and applications [PDF]
Proceedings of the American Mathematical Society, 1997 Let \(H\) be a pointed Hopf algebra over an algebraically closed field of characteristic zero. The author's main result is that if \(H\) is not semisimple, then \(H\) contains a group-like element \(g\) and a \((g,1)\)-skew primitive element \(x\), with specific algebraic relations including \(gx=qxg\), \(q\) a primitive root of unity.
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COQUASITRIANGULAR STRUCTURES FOR EXTENSIONS OF HOPF ALGEBRAS. APPLICATIONS [PDF]
Glasgow Mathematical Journal, 2012 AbstractLet A ⊆ E be an extension of Hopf algebras such that there exists a normal left A-module coalgebra map π : E → A that splits the inclusion. We shall describe the set of all coquasitriangular structures on the Hopf algebra E in terms of the datum (A, E, π) as follows: first, any such extension E is isomorphic to a unified product A ⋉ H, for some
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Hopf algebra actions on differential graded algebras and applications
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011 to appear in Bull. Belg.
He, Ji-Wei +2 more
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Techniques for Classifying Hopf Algebras and Applications to Dimensionp3 [PDF]
Communications in Algebra, 2013 19 ...
Beattie, M., García, Gastón Andrés
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