Results 41 to 50 of about 41,540 (204)

Character groups of Hopf algebras as infinite-dimensional Lie groups [PDF]

, 2015
In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional Lie group structure on the character group with values in ...
Bogfjellmo, Geir, Dahmen, Rafael, Schmeding, Alexander   +2 more
core   +3 more sources

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   +2 more sources

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

Co-Poisson structures on polynomial Hopf algebras

, 2017
The Hopf dual $H^\circ$ of any Poisson Hopf algebra $H$ is proved to be a co-Poisson Hopf algebra provided $H$ is noetherian. Without noetherian assumption, it is not true in general.
Lou, Qi, Wu, QuanShui
core   +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

Relating two Hopf algebras built from an operad [PDF]

, 2007
Starting from an operad, one can build a family of posets. From this family of posets, one can define an incidence Hopf algebra. By another construction, one can also build a group directly from the operad. We then consider its Hopf algebra of functions.
Chapoton, Frédéric, Livernet, Muriel
core   +3 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

The doubles of a braided Hopf algebra

, 2012
Let A be a Hopf algebra in a braided rigid category B. In the case B admits a coend C, which is a Hopf algebra in B, we defined in 2008 the double D(A) of A, which is a quasitriangular Hopf algebra in B whose category of modules is isomorphic to the ...
Bruguières, Alain, Virelizier, Alexis
core   +3 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