Femić, Bojana Mejía Castaño, Adriana Mombelli, Martín
Published in
Journal of Pure and Applied Algebra

For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal(H)→BrPic(Rep(H)), from the group of equivalence classes of H-biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H=Tq is a Taft Hopf algebra and for this ...

Femić, Bojana Mejía Castaño, Adriana Mombelli, Martín
Published in
Journal of Pure and Applied Algebra

CAO, Haijun LI, Fang ZHANG, Mianmian
Published in
Acta Mathematica Scientia

CAO, Haijun LI, Fang ZHANG, Mianmian
Published in
Acta Mathematica Scientia

The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S = [Y;Gα, φα,β] by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal.

Sommerhäuser, Yorck Zhu, Yongchang
Published in
Advances in Mathematics

For a semisimple factorizable Hopf algebra over a field of characteristic zero, we show that the value that an integral takes on the inverse Drinfel’d element differs from the value that it takes on the Drinfel’d element itself by at most a fourth root of unity. This can be reformulated by saying that the central charge of the Hopf algebra is an in...

Foissy, L.
Published in
Advances in Mathematics

We study the self-dual Hopf algebra HSP of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from HSP to the Hopf algebra of free quasi-symmetric functions FQSym given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to FQSym; the first one is based on plane posets, the second ...

Bakalov, Bojko D'Andrea, Alessandro Kac, Victor G.

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[\partial] is replaced by the universal enveloping algebra H of a finite-...

Foissy, Loïc
Published in
Advances in Mathematics

We consider systems of combinatorial Dyson–Schwinger equations in the Connes–Kreimer Hopf algebra H I of rooted trees decorated by a set I. Let H ( S ) be the subalgebra of H I generated by the homogeneous components of the unique solution of this system. If it is a Hopf subalgebra, we describe it as the dual of the enveloping algebra of a Lie alge...

Foissy, Loïc
Published in
Advances in Mathematics

We consider systems of combinatorial Dyson–Schwinger equations (briefly, SDSE) X 1 = B 1 + ( F 1 ( X 1 , … , X N ) ) , … , X N = B N + ( F N ( X 1 , … , X N ) ) in the Connes–Kreimer Hopf algebra H I of rooted trees decorated by I = { 1 , … , N } , where B i + is the operator of grafting on a root decorated by i, and F 1 , … , F N are non-constant ...

Pfeiffer, Hendryk

We show that every essentially small finitely semisimple k-linear additive spherical category in which k=End(1) is a field, is equivalent to its dual over the long canonical forgetful functor. This includes the special case of modular categories. In order to prove this result, we show that the universal coend of the spherical category with respect ...