Show simple item record Gohm, Rolf Köstler, Claus Michael 2010-01-11T18:26:52Z 2010-01-11T18:26:52Z 2009-07-01
dc.identifier.citation Gohm , R & Köstler , C M 2009 , ' Noncommutative Independence from the Braid Group B∞ ' Communications in Mathematical Physics , vol 289 , no. 2 , pp. 435-482 . DOI: 10.1007/s00220-008-0716-x en
dc.identifier.issn 0010-3616
dc.identifier.other PURE: 143115
dc.identifier.other PURE UUID: 7feca3d4-a51c-47b4-b0cb-c6f8d58a211c
dc.identifier.other dspace: 2160/3975
dc.identifier.other DSpace_20121128.csv: row: 3356
dc.identifier.other RAD: 1928
dc.identifier.other RAD_Outputs_All_ID_Import_20121105.csv: row: 1060
dc.identifier.other Scopus: 67349257936
dc.identifier.uri en
dc.description Comm. Math. Phys., vol.289(2) (2009), 435-482 en
dc.description.abstract We introduce `braidability' as a new symmetry for (infinite) sequences of noncommutative random variables related to representations of the braid group $B_\infty$. It provides an extension of exchangeability which is tied to the symmetric group $S_\infty$. Our key result is that braidability implies spreadability and thus conditional independence, according to the noncommutative extended de Finetti theorem (of C. K\'{o}stler). This endows the braid groups $B_n$ with a new intrinsic (quantum) probabilistic interpretation. We underline this interpretation by a braided extension of the Hewitt-Savage Zero-One Law. Furthermore we use the concept of product representations of endomorphisms (of R. Gohm) with respect to certain Galois type towers of fixed point algebras to show that braidability produces triangular towers of commuting squares and noncommutative Bernoulli shifts. As a specific case we study the left regular representation of $B_\infty$ and the irreducible subfactor with infinite Jones index in the non-hyperfinite $II_1$-factor $L(B_\infty)$ related to it. Our investigations reveal a new presentation of the braid group $B_\infty$, the `square root of free generator presentation' $F_\infty^{1/2}$. These new generators give rise to braidability while the squares of them yield a free family. Hence our results provide another facet of the strong connection between subfactors and free probability theory and we speculate about braidability as an extension of (amalgamated) freeness on the combinatorial level. en
dc.format.extent 48 en
dc.language.iso eng
dc.relation.ispartof Communications in Mathematical Physics en
dc.rights en
dc.title Noncommutative Independence from the Braid Group B∞ en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.contributor.institution Department of Physics en
dc.description.status Peer reviewed en

Files in this item

Aside from theses and in the absence of a specific licence document on an item page, all works in Cadair are accessible under the CC BY-NC-ND Licence. AU theses and dissertations held on Cadair are made available for the purposes of private study and non-commercial research and brief extracts may be reproduced under fair dealing for the purpose of criticism or review. If you have any queries in relation to the re-use of material on Cadair, contact

This item appears in the following Collection(s)

Show simple item record

Search Cadair

Advanced Search