Quantum stochastic convolution cocycles —algebraic and $C^*$-algebraic
Volume 73 / 2006
Banach Center Publications 73 (2006), 313-324
MSC: Primary 81S25; Secondary 16W30.
DOI: 10.4064/bc73-0-24
Abstract
We summarise recent results concerning quantum stochastic convolution cocycles in two contexts—purely algebraic and $C^*$-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and $C^*$-algebraic situations is emphasised; the final section treats the unifying example of convolution cocycles on full compact quantum groups.
