Braided bialgebras were defined by mimicking the definition of bialgebras in a braided category; see [Ta]. In this paper we are interested in those braided bialgebras that are connected as a coalgebra, and such that, up to multiplication by a certain scalar, their braiding restricted to the primitive part is a Hecke operator. To every braided bialgebra as above we associate a braided Lie algebr...

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here and in [6] that operator algebras with r.c.a.i. should be studied in terms of a certain left ideal of a C∗-algebra. We study operator algebras and their multiplier algebras from the perspective of ‘Hamana theory’ and using the multiplier algebras...

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...