Projects per year
Abstract
As left adjoint to the dual algebra functor, Sweedler’s finite dual construction is an important tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the dual algebra functor, which exists over arbitrary rings, shares a number of properties with the finite dual. Nonetheless the requirement that it should map Hopf algebras to Hopf algebras needs the extra assumption that this left adjoint should map an algebra into its linear dual. We identify a condition guaranteeing that Sweedler’s construction works when generalized to noetherian commutative rings. We establish the following two apparently previously unnoticed dual adjunctions: For every commutative ring R the left adjoint of the dual algebra functor on the category of Rbialgebras has a right adjoint. This dual adjunction can be restricted to a dual adjunction on the category of Hopf Ralgebras, provided that R is noetherian and absolutely flat.
Original language  English 

Pages (fromto)  619647 
Number of pages  29 
Journal  Applied Categorical Structures 
Volume  24 
Issue number  5 
DOIs  
Publication status  Published  1 Oct 2016 
Keywords
 Hopf algebra
 coalgebra
 Sweedler dual
 finite dual coalgebra
 monoidal functor
Fingerprint Dive into the research topics of 'Generalizations of the Sweedler dual'. Together they form a unique fingerprint.
Projects
 1 Finished

Structural homotopy theory: a categorytheoretic study
Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M. (.
1/01/13 → 31/12/16
Project: Research