Results 31 to 40 of about 600 (187)

Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration

Forum of Mathematics, Sigma
In this paper, we introduce the notion of post-Hopf algebroids, generalizing the pre-Hopf algebroids introduced in [8] in the study of exotic aromatic S-series. We construct action post-Hopf algebroids through actions of post-Hopf algebras.
Adrien Busnot Laurent, Yunnan Li, Yunhe Sheng   +2 more
doaj   +1 more source

The Cambrian Hopf Algebra [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees.
G. Chatel, V. Pilaud
doaj   +1 more source

A Hopf module characterization of Hopf algebras [PDF]

Proceedings of the American Mathematical Society, 1983
A bialgebra over a field is a Hopf algebra if and only if all (nonzero) right Hopf modules are free, as modules, on a set of invariants.
openaire   +2 more sources

Hopf Algebra Symmetries of an Integrable Hamiltonian for Anyonic Pairing

Axioms, 2012
Since the advent of Drinfel’d’s double construction, Hopf algebraic structures have been a centrepiece for many developments in the theory and analysis of integrable quantum systems.
Jon Links
doaj   +1 more source

Multiplier Left Hopf Algebras

Mathematics
In this paper, we introduce and study the notion of a multiplier left Hopf algebra, which can be seen as an extension of the Van Daele’s multiplier Hopf algebras and the Green–Nichols–Taft’s left Hopf algebras.
Chunxiao Yan, Shuanhong Wang
doaj   +1 more source

Method of general Coule–Hopf substitutions in theory of finite-dimensional dynamical systems

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011
We consider the results of applying the method of generic Cole–Hopf substitutions to integration of finite-dimensional dynamical systems. Dynamical systems are represented in the form of matrix ordinary differential equations with specific matrix algebra
C. S. Obrubov, V. M. Zhuravlev
doaj   +1 more source

On indicators of Hopf algebras [PDF]

Israel Journal of Mathematics, 2015
Kashina, Montgomery and Ng introduced the $n$-th indicator $ν_n(H)$ of a finite-dimensional Hopf algebra $H$ and showed that the indicators have some interesting properties such as the gauge invariance. The aim of this paper is to investigate the properties of $ν_n$'s. In particular, we obtain the cyclotomic integrality of $ν_n$ and a formula for $ν_n$
openaire   +2 more sources

Rota–Baxter Operators on Cocommutative Weak Hopf Algebras

Mathematics, 2021
In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H.
Zhongwei Wang, Zhen Guan, Yi Zhang, Liangyun Zhang   +3 more
doaj   +1 more source

Quiver Hopf algebras

Journal of Algebra, 2004
If \(Q\) is a Schurian Hopf quiver and \(k\) is a field of characteristic zero, the simple pointed Hopf subalgebras of a graded Hopf algebra structure on the path coalgebra \(kQ^c\) are classified. A dual Gabriel theorem for pointed Hopf algebras is proved.
Van Oystaeyen, Fred, Zhang, Pu
openaire   +3 more sources

Compact Manifolds With Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has a uniformly almost nilpotent fundamental group. Leftover questions and conjectures, have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples (Mk9,gk)$(
Elia Bruè, Aaron Naber, Daniele Semola
wiley   +1 more source