Related papers: Frobenius extensions and weak Hopf algebras

A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and…

For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a…

Let $H$ be a finite dimensional semisimple Hopf algebra, $A$ a differential graded (dg for short) $H$-module algebra. Then the smash product algebra $A\#H$ is a dg algebra. For any dg $A\#H$-module $M$, there is a quasi-isomorphism of dg…

In this paper, we obtain a canonical central element $\nu_H$ for each semi-simple quasi-Hopf algebra $H$ over any field $k$ and prove that $\nu_H$ is invariant under gauge transformations. We show that if $k$ is algebraically closed of…

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), U_q(sl2) and the enveloping…

For a bialgebra $L$ coacting on a $\Bbbk$-algebra $A$, a classical result states that $A$ is a right $L$-comodule algebra if and only if $A$ is an algebra in the monoidal category $\mathcal{M}^{L}$ of right $L$-comodules; the former notion…

We study the representations and their Frobenius-Schur indicators of two semisimple Hopf algebras related to the symmetric group $S_n$, namely the bismash products $H_n = k^{C_n}# kS_{n-1}$ and its dual $J_n = k^{S_{n-1}}# kC_n = (H_n)^*,$…

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective. For a separable Frobenius extension between Artin algebras,…

Multiplier Hopf algebroids are algebraic versions of quantum groupoids that generalize Hopf algebroids to the non-unital case and weak (multiplier) Hopf algebras to non-separable base algebras. The main structure maps of a multiplier Hopf…

The tensor functor called $\alpha$-induction arises from a Frobenius algebra object, or a Q-system, in a braided unitary fusion category. In the operator algebraic language, it gives extensions of endomorphism of $N$ to $M$ arising from a…

For von Neumann algebras M, N not isomorphic to C^2 and without type I_2 summands, we show that for an order-isomorphism f:AbSub(M)->AbSub(N) between the posets of abelian von Neumann subalgebras of M and N, there is a unique Jordan…

An algebra extension $A \| B$ is right depth two in this paper if its tensor-square is $A$-$B$-isomorphic to a direct summand of any (not necessarily finite) direct sum of $A$ with itself. For example, normal subgroups of infinite groups,…

We study Kan extensions in three weakenings of the Eilenberg-Moore double category associated to a double monad, that was introduced by Grandis and Par\'e. To be precise, given a normal oplax double monad $T$ on a double category $\mathcal…

We identify additional structure on a conservative lax monoidal functor from a closed monoidal category $\mathcal{C}$ to a Grothendieck-Verdier category $\mathcal{D}$, such that the Grothendieck-Verdier structure of $\mathcal{D}$ lifts to…

We investigate the transformed Hopf algebras in Hopf Galois extensions. The final goal of this paper is to introduce certain triangular Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic $p>0$.

We survey some aspects of Frobenius algebras, Frobenius structures and their relation to finite Hopf algebras using graphical calculus. We focus on the `yanking' moves coming from a closed structure in a rigid monoidal category, the…

In this paper, we introduce and study the notion of cointegrals in a weak multiplier Hopf algebras $(A, \Delta)$. A cointegral is a non-zero element $h$ in the multiplier algebra $M(A)$ such that $ah=\v_t(a)h$ for any $a\in A$. When $A$ has…

Given a finite depth subfactor planar algebra $\mathcal{P}$ endowed with the graded $*$-algebra structures $\{Gr_k^+ \mathcal{P}\}_{k\in\mathbb{N}}$ of Guionnet, Jones, and Shlyakhtenko, there is a sequence of canonical traces $Tr_{k,+}$ on…

We study monoidal comonads on a naturally Frobenius map-monoidale $M$ in a monoidal bicategory $\mathcal M$. We regard them as bimonoids in the duoidal hom-category $\mathcal M(M,M)$, and generalize to that setting various conditions…