Science Home >
Math and Stats Home
>
All Events
>
2018
>
November
> Operator Algebras Seminar (Ketelboeter)

Operator Algebra Seminars
Fri., Nov. 2, 2018 1:30 p.m. - Fri., Nov. 2, 2018 2:30 p.m.
Location: Classroom Building (CL) 416
Speaker: Brian Ketelboeter
Title: C*-Convolutive Systems II
Abstract:
A $C^*$-quantum convolutive system consists of a family of $C^*$-algebras $\{\mathcal{A}_{s,t}\}$,
given for all $s, t \in\mathbb{R}$, $s < t$, along with morphisms $\Delta_{r,s,t}: \mathcal{A}_{r,t}\to \mathcal{A}_{r,s}\otimes \mathcal{A}_{s,t}$ given for all
$r, s, t \in\mathbb{R}$, $r < s < t$, satisfying the co-associativity condition:
\begin{eqnarray*}\label{qcs}\left(\operatorname{id}_{\mathcal{A}_{r,s}}\otimes \Delta_{s,t,u}\right)\Delta_{r,s,u}=
\left( \Delta_{r,s,t}\otimes \operatorname{id}_{\mathcal{A}_{t,u}} \right)\Delta_{r,t,u}\end{eqnarray*}
whenever $r, s, t, u\in\mathbb{R}$, $r < s < t < u$.
We continue our discussion of convolutive systems; including the definitions and our first example.
given for all $s, t \in\mathbb{R}$, $s < t$, along with morphisms $\Delta_{r,s,t}: \mathcal{A}_{r,t}\to \mathcal{A}_{r,s}\otimes \mathcal{A}_{s,t}$ given for all
$r, s, t \in\mathbb{R}$, $r < s < t$, satisfying the co-associativity condition:
\begin{eqnarray*}\label{qcs}\left(\operatorname{id}_{\mathcal{A}_{r,s}}\otimes \Delta_{s,t,u}\right)\Delta_{r,s,u}=
\left( \Delta_{r,s,t}\otimes \operatorname{id}_{\mathcal{A}_{t,u}} \right)\Delta_{r,t,u}\end{eqnarray*}
whenever $r, s, t, u\in\mathbb{R}$, $r < s < t < u$.
We continue our discussion of convolutive systems; including the definitions and our first example.