Related papers: Hopf algebras for matroids over hyperfields
In this paper, we introduce and investigate \emph{bisemialgebras}and\emph{\ Hopf semialgebras} over commutative semirings. We generalize to the semialgebraic context several results on bialgebras and Hopf algebras over rings including the…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
We define and investigate pairings of multiplier Hopf algebras. It is shown that two dually paired regular multiplier Hopf ($*$-)algebras $A$ and $B$ yield a quantum double multiplier Hopf ($*$-)algebra which is again regular. Integrals on…
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for…
The theory of Doi-Hopf modules is generalized to Weak Hopf algebras.
A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…
We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf…
Let k be a field. Let also (F, G) be a matched pair of groups. We give necessary and sufficient conditions on a pair (\sigma, \tau) of 2-cocycles in order that the crossed product algebra and the crossed coproduct coalgebra…
Some new results on the module structure of Hopf algebras over a certain class of Hopf subalgebras and right coideal subalgebras are proved.
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…
In this paper, we introduce the notions of Hopf group braces, post-Hopf group algebras and Rota-Baxter Hopf group algebras as important generalizations of Hopf brace, post Hopf algebra and Rota-Baxter Hopf algebras respectively. We also…
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…
The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial…
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more…
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…
We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf…
In this short note we make a few remarks on a class of generalized incidence matrices whose matroids do not depend on the orientation of the underlying graph and natural commutative algebras associated to such matrices.
We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…
We characterize the shifted simple graphs and the $3$-uniform shifted hypergraphs whose inverse image under exterior shifting is the set of bases of a matroid: those are exactly the hypergraphs whose hyperedges form an initial lex-segment.…