Generalized braided quantum groups

Abstract

A generalization of Hopf algebras (quantum groups), and braided-Hopf algebras (braided quantum groups) in which the multiplicativity axiom for the counit is dropped, is presented. The generalization overcomes an inherent geometrical inhomogeneity of standard quantum groups and braided quantum groups, in the sense of allowing completely ‘pointless’ objects. All braid-type equations appear as a consequence of deeper axioms. Braided counterparts of basic algebraic relations between fundamental entities of the standard theory are found.