Group-Graded By-Product Construction and Group Double Centralizer Properties
-
Published:2022-08-15
Issue:16
Volume:10
Page:2943
-
ISSN:2227-7390
-
Container-title:Mathematics
-
language:en
-
Short-container-title:Mathematics
Author:
Zhang Senlin,Wang Shuanhong
Abstract
For a group π with unit e, we introduce and study the notion of a π-graded Hopf algebra. Then we introduce and construct a new braided monoidal category HHeYDπ over a π-graded Hopf algebra H. We introduce the notion of a π-double centralizer property and investigate this property by studying a braided π-graded Hopf algebra U(gln(V))⋉πH, where V is an n-dimensional vector space in HHeYDπ and U(gln(V)) is the braided universal enveloping algebra of gln(V) which is not the usual Hopf algebra. Finally, some examples and special cases are given.
Funder
the National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference16 articles.
1. Categories for the Working Mathematician;Lane,1971
2. Representation Theory;Fulton,1991
3. Hook young diagrams with applications to combinatorics and to representations of Lie superalgebras
4. Hopf Algebras;Sweedler,1969
5. Algebras and Hopf algebras in braided categories;Majid,1994