# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Quantum stochastic convolution cocycles —algebraic and $C^*$-algebraic

### Tom 73 / 2006

Banach Center Publications 73 (2006), 313-324 MSC: Primary 81S25; Secondary 16W30. DOI: 10.4064/bc73-0-24

#### Streszczenie

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.

#### Autorzy

• J. Martin LindsayDepartment of Mathematics and Statistics
Lancaster University
Lancaster LA1 4YF, U.K.
e-mail
• Adam G. SkalskiDepartment of Mathematics and Statistics
Lancaster University
Lancaster LA1 4YF, U.K.
e-mail

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