相关论文: Noetherian Hopf algebras

In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there…

We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.

In this article we discuss the Hopf algebras spanned by the adjacency matrices in detail. We show that there two Hopf algebraic structures concerning the adjacency matrices, one is the copy of Connes-Kreimer Hopf algebra, another one is the…

We give a definition and study Hopf structures in ternary (and n-ary) Nambu-Lie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra and Hopf 3- algebra are introduced. Some examples of Hopf structures are analyzed.

The collection of open sets of a topological space forms a Heyting algebra, which leads to the idea of a Heyting algebra as a generalized topological space. In fact, a sober topological space may be reconstructed from its locale of open…

We present an unified construction for algebras and modules homologies and cohomologies, in the case of associative, commuttaive, Lie and Gerstenhaber algebras. We make a distinction between the linear part of the construction of algebras…

We summarize here the first results obtained using a technique we recently developed for the Noether analysis of Hopf-algebra spacetime symmetries, including the derivation of conserved charges for field theories in noncommutative…

We review old and new properties of Hopf manifolds from the point of view of their analytic and metric structure.

We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.

We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.

We develop some basic homological theory of hopfological algebra as defined by Khovanov. Several homological properties in hopfological algebra analogous to those of usual homological theory of DG algebras are obtained.

We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.

The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and…

The purpose of this paper is to provide a cohomology of $n$-Hom-Leibniz algebras. Moreover, we study some higher operations on cohomology spaces and deformations.

This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and…

In this article, we use the theory of (non-abelian) exterior product of Hom-Lie algebras to prove the Hopf formula for these algebras. As an application, we construct an eight-term sequence in the homology of Hom-Lie algebras. We also…

The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted by homomorphisms. We discuss…

By omitting the unitary constraint from the definition of weak post-Hopf algebras, we introduce the concept of relaxed weak post-Hopf algebras, offering a thorough characterization of all feasible relaxed weak post-Hopf algebraic structures…

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…

This paper introduces Hopf braces, a new algebraic structure related to the Yang-Baxter equation which include Rump's braces and their non-commutative generalizations as particular cases. Several results of classical braces are still valid…