Rocky Mountain Journal of Mathematics

Semi-cosimplicial objects and spreadability

D. Gwion Evans, Rolf Gohm, and Claus Köstler

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Abstract

To a semi-cosimplicial object (SCO) in a category, we associate a system of partial shifts on the inductive limit. We show how to produce an SCO from an action of the infinite braid monoid $\mathbb{B} ^+_\infty $ and provide examples. In categories of (noncommutative) probability spaces, SCOs correspond to spreadable sequences of random variables; hence, SCOs can be considered as the algebraic structure underlying spreadability.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1839-1873.

Dates
First available in Project Euclid: 21 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1511254955

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-1839

Mathematical Reviews number (MathSciNet)
MR3725247

Zentralblatt MATH identifier
06816573

Subjects
Primary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 20F36: Braid groups; Artin groups 46L53: Noncommutative probability and statistics

Keywords
Semi-cosimplicial object coface operator partial shift braid monoid cohomology noncommutative probability space spreadability subfactor

Citation

Evans, D. Gwion; Gohm, Rolf; Köstler, Claus. Semi-cosimplicial objects and spreadability. Rocky Mountain J. Math. 47 (2017), no. 6, 1839--1873. doi:10.1216/RMJ-2017-47-6-1839. https://projecteuclid.org/euclid.rmjm/1511254955


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