Weak multiplier bialgebras

Abstract

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the ‘base algebras’) are shown to carry coseparable co-Frobenius coalgebra structures. Appropriate modules over a nice enough weak multiplier bialgebra are shown to constitute a monoidal category via the (co)module tensor product over the base (co)algebra. The relation to Van Daele and Wang’s (regular and arbitrary) weak multiplier Hopf algebra is discussed.