Related papers: Hopf algebraic techniques applied to super algebra…
We consider issues related to the origins, sources and initial motivations of the theory of Hopf algebras. We consider the two main sources of primeval development: algebraic topology and algebraic group theory. Hopf algebras are named from…
We say that a Hopf algebra H is semicocommutative if the right adjoint coaction factorizes through the tensor product of H with the center of H. For instance the commutative and the cocommutative Hopf algebras are semicocommutative. The…
We study actions of pointed Hopf algebras on matrix algebras. Our approach is based on known facts about group gradings of matrix algebras.
We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra.
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
In this paper we classify, up to equivalence, all semisimple nontrivial Hopf algebras of dimension $2^{2n+1}$ for $n\geq 2$ over an algebraically closed field of characteristic $0$ with the group of group-like elements isomorphic to…
We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We…
We define a super version of the Connes-Moscovici Hopf algebra, $\mathcal{H}_1$. For that, we consider the supergroup $G^s=Diff^+(\mathbb{R}^{1,1})$ of orientation preserving diffeomorphisms of the superline $\mathbb{R}^{1,1}$ and define…
We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal…
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as…
We introduce a notion of Hopf-Lie-Rinehart algebra and show that the universal algebra of a Hopf-Lie-Rinehart algebra acquires an ordinary Hopf algebra structure.
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these…
In a recent paper (1994 {\sl J.\ Phys.\ A: Math.\ Gen.\ }{\bf 27} 5907), Oh and Singh determined a Hopf structure for a generalized $q$-oscillator algebra. We prove that under some general assumptions, the latter is, apart from some…
Let $\mathbb{K}$ be the set of hybrid numbers. This paper is to look for all the weak Hopf structures on $\mathbb{K}$. Once $\mathbb{K}$ is endowed with a structure of a weak Hopf algebra, we shall compute the source algebra and target…
We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…
We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov's construction of higher Bloch groups. We…
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
In this paper we introduce the notion of weak Hopf quasigroup as a generalization of weak Hopf algebras and Hopf quasigroups. We obtain its main properties and we prove the fundamental theorem of Hopf modules for these algebraic structures.
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…