Interacting Hopf algebras: the string diagrammatic theory of linear subspaces

Fabio Zanasi
University College London

Date(s) : 18/06/2015   iCal
11 h 00 min - 12 h 00 min

We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack’s approach to composing PROPs: they feature two Hopf algebras and two Frobenius algebras. This construction is instrumental in showing that IH is a presentation by generators and equations of the PROP of linear relations (i.e. subspaces) over the field of fractions of R.
The equational theory IH turns out to be useful in various contexts. For R=Z, it expresses rational subspaces. The case R=Z_2 is of importance for describing quantum computation. In this talk we will focus on the case R=k[x], in which IH yields a compositional stream semantics for linear dynamical systems (signal flow graphs).


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