Cosovereign Hopf algebras

A sovereign monoidal category is an autonomous monoidal category endowed with the choice of an autonomous structure and an isomorphism of monoidal functors between the associated left and right duality functors. In this paper we define and study the algebraic counterpart of sovereign monoidal categories: cosovereign Hopf algebras. We describe the universal cosovereign Hopf algebras, we study finite-dimensional cosovereign Hopf algebras via the dimension theory provided by the sovereign structure and we examine an example generalizing the quantum groups SLq.