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# 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.