Weak multiplier bialgebras

Böhm, Gabriella Eszter and Gomez-Torrecillas, J. and Lopez-Centella, E. (2015) Weak multiplier bialgebras. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 367 (12). pp. 8681-8721. ISSN 0002-9947

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Abstract

A non-unital generalization of weak bialgebra is proposed with a multi- plier-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 weak multiplier bialgebra are shown to consti- tute 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.

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