Related papers: Hopf automorphisms and twisted extensions
We show that various cyclic and cocyclic modules attached to Hopf algebras and Hopf modules are related to each other via Connes' duality isomorphism for the cyclic category.
Given a cocommutative Hopf algebra $\mathcal{H}$ over a commutative ring $K$ and a symmetric partial action of $\mathcal{H}$ on a $K$-algebra $A,$ we obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild…
We extend the previously established zesting techniques from fusion categories to general tensor categories. In particular we consider the category of comodules over a Hopf algebra, providing a detailed translation of the categorical…
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…
We introduce the concept of a $\lambda$-Hopf algebra as a Hopf algebra obtained as the partial smash product algebra of a Hopf algebra and its base field, and show that every Hopf algebra is a $\lambda$-Hopf algebra. Moreover, a method to…
We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^\delta\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat…
The correspondence between Lie algebras, Lie groups, and algebraic groups, on one side and commutative Hopf algebras on the other side are known for a long time by works of Hochschild-Mostow and others. We extend this correspondence by…
We study the de-equivariantization of a Hopf algebra by an affine group scheme and we apply Tannakian techniques in order to realize it as the tensor category of comodules over a coquasi-bialgebra. As an application we construct a family of…
Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is…
We re-examine all the contractions related with the ${\cal U}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$ as an…
We introduce the Frobenius-Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius-Schur theorem, including that for semisimple quasi-Hopf algebras, weak Hopf…
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, aswell as colour-Lie algebras. Basic facts about braided categories C…
We systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal…
We settle in this paper a question left open in our paper ``Modular Hecke algebras and their Hopf symmetry'', by showing how to extend the Rankin-Cohen brackets from modular forms to modular Hecke algebras. More generally, our procedure…
In this paper, we completely determine the group of algebra automorphisms for the two-parameter Hopf algebra ${\check U}_{r,s}^{\geq 0}({\mathfrak sl_{3}})$. As a result, the group of Hopf algebra automorphisms is determined for $\V$ as…
Using cocommutativity of the Hopf algebra of symmetric functions, certain skew Schur functions are proved to be equal. Some of these skew Schur function identities are new.
We construct a Hopf algebra on integer binary relations that contains under the same roof several well-known Hopf algebras related to the permutahedra and the associahedra: the Malvenuto-Reutenauer algebra on permutations, the Loday-Ronco…
In this note we discuss the possibility of constructing the cosimplicial complex for the multiplier Hopf algebras and extending the cyclicity operator to obtain the Hopf-cyclic cohomology for them. We show that the definition of modular…
In this paper, we give an explicit chain map, which induces the algebra isomorphism between the Hochschild cohomology ${\bf HH}^{\bullet}(B)$ and the $H$-invariant subalgebra ${\bf H}^{\bullet}(A, B)^{H}$ under two mild hypotheses, where…
Let $H$ be a Hopf algebra. Ju and Cai introduced the notion of twisting of an $H$-module coalgebra. In this note, we study the relationship between twistings, crossed coproducts and Hopf-Galois coextensions. In particular, we show that a…