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Hopf algebras in noncommutative geometry
(2003)
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal ...
Finite presentability and the homological type FPm for a class of Hopf algebras
(Taylor & Francis IncPhiladelphiaEUA, 2006)
Pares admissíveis, sistemas admissíveis e biálgebras na categoria dos módulos de Yetter-Drinfeld
(Universidade Federal de Santa MariaBRMatemáticaUFSMPrograma de Pós-Graduação em Matemática, 2014-03-19)
The purpose of this work is to study the relationships between admissible pairs, systems admissible and bialgebras in the category of Yetter-Drinfeld modules, as well as some properties of the Hopf algebra associated (via ...
Introdução à álgebra de Hopf
(Universidade Tecnológica Federal do ParanáToledoBrasilLicenciatura em MatemáticaUTFPR, 2018-12-07)
The purpose of this work is to present the studies realized about algebras, coalgebras and bialgebras, culminating in the definition of Hopf algebras. Examples of each algebraic structures, as well as counterexamples when ...
Faà di Bruno Hopf algebras
(2022-11)
This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure allows, among several other things, a short proof of ...
Classifying Hopf algebras of a given dimension
(2013-01)
Classifying all Hopf algebras of a given finite dimension over C is a challenging problem which remains open even for many small dimensions, not least because few general approaches to the problem are known. Some useful ...