Constructing Quasitriangular Hopf Algebras

Autor:	Quanguo Chen, Dingguo Wang
Rok vydání:	2015
Předmět:	Algebra and Number Theory Direct sum of modules Coalgebra Mathematics::Rings and Algebras Coproduct Quasitriangular Hopf algebra Hopf algebra Bialgebra Algebra Set (abstract data type) Mathematics::Category Theory Mathematics::Quantum Algebra Bijection Mathematics
Zdroj:	Communications in Algebra. 43:1698-1722
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927872.2013.876036
Popis:	This paper is devoted to constructing quasitriangular bialgebras (or Hopf algebras). The tool we use is a new coproduct, we call it the unified coproduct, in the construction of which a Hopf algebra and an algebra are connected by three algebra maps: two coactions and a generalized cocycle. Both the crossed coproduct of a bialgebra coacting on a coalgebra and the bicrossed coproduct of two bialgebras are special cases of the unified coproduct. Then we establish a bijective correspondence between the set of all quasitriangular structures on the arbitrary unified coproduct and a certain set of datum related to the components of the unified coproduct. As the main application, we derive the necessary and sufficient conditions for the crossed coproduct (or bicrossed coproduct) to be a quasitriangular Hopf algebra.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::23b5c0890bcd8d6997efa911cc18f1af https://doi.org/10.1080/00927872.2013.876036 Zobrazit plný text záznamu