Algebraic structures in comodule categories over weak bialgebras. Issue 7 (3rd July 2022)

• Record Type: Journal Article
• Authors: Walton, Chelsea; Wicks, Elizabeth; Won, Robert
• Is Part Of: Communications in algebra. Volume 50:Issue 7(2022)
• Page Start: 2877
• Page End: 2910
• Publication Date: 2022-07-03
• Subjects: Corepresentation category -- quantum transformation groupoid -- weak bialgebra -- weak Hopf algebra; 16T05 -- 18M05 -- 16T15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.2022155
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: For a bialgebra L coacting on a k -algebra A, a classical result states A is a right L -comodule algebra if and only if A is an algebra in the category M L of right L -comodules. We generalize this to the setting of weak bialgebras H . We prove that there is an isomorphism between the categories of right H -comodule algebras and the category of algebras in M H . We also recall and introduce the formulaic notion of H coacting on a k -coalgebra and on a Frobenius k -algebra, respectively, and prove analogous category isomorphisms. Many examples are provided throughout.