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Invariants for E_0-semigroups on II_1 factors

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Invariants for E_0-semigroups on II_1 factors. / Margetts, Oliver; Srinivasan, R.
In: Communications in Mathematical Physics, Vol. 323, No. 3, 11.2013, p. 1155-1184.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Margetts, O & Srinivasan, R 2013, 'Invariants for E_0-semigroups on II_1 factors', Communications in Mathematical Physics, vol. 323, no. 3, pp. 1155-1184. https://doi.org/10.1007/s00220-013-1790-2

APA

Margetts, O., & Srinivasan, R. (2013). Invariants for E_0-semigroups on II_1 factors. Communications in Mathematical Physics, 323(3), 1155-1184. https://doi.org/10.1007/s00220-013-1790-2

Vancouver

Margetts O, Srinivasan R. Invariants for E_0-semigroups on II_1 factors. Communications in Mathematical Physics. 2013 Nov;323(3):1155-1184. doi: 10.1007/s00220-013-1790-2

Author

Margetts, Oliver ; Srinivasan, R. / Invariants for E_0-semigroups on II_1 factors. In: Communications in Mathematical Physics. 2013 ; Vol. 323, No. 3. pp. 1155-1184.

Bibtex

@article{4e9b8e82ab0d4e9d939af0fb7bacfa21,
title = "Invariants for E_0-semigroups on II_1 factors",
abstract = "We introduce four new cocycle conjugacy invariants for $E_0$-semigroups on II$_1$ factors: a coupling index, a dimension for the gauge group, a \emph{super product system} and a $C^*$-semiflow. Using noncommutative It\^o integrals we show that the dimension of the gauge group can be computed from the structure of the \emph{additive cocycles}. We do this for the Clifford flows and even Clifford flows on the hyperfinite \twoone factor, and for the free flows on the free group factor $L(F_\infty)$. In all cases the index is $0$, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the $C^*$-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate \en-semigroups.",
author = "Oliver Margetts and R. Srinivasan",
note = "The original publication is available at www.link.springer.com",
year = "2013",
month = nov,
doi = "10.1007/s00220-013-1790-2",
language = "English",
volume = "323",
pages = "1155--1184",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

RIS

TY - JOUR

T1 - Invariants for E_0-semigroups on II_1 factors

AU - Margetts, Oliver

AU - Srinivasan, R.

N1 - The original publication is available at www.link.springer.com

PY - 2013/11

Y1 - 2013/11

N2 - We introduce four new cocycle conjugacy invariants for $E_0$-semigroups on II$_1$ factors: a coupling index, a dimension for the gauge group, a \emph{super product system} and a $C^*$-semiflow. Using noncommutative It\^o integrals we show that the dimension of the gauge group can be computed from the structure of the \emph{additive cocycles}. We do this for the Clifford flows and even Clifford flows on the hyperfinite \twoone factor, and for the free flows on the free group factor $L(F_\infty)$. In all cases the index is $0$, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the $C^*$-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate \en-semigroups.

AB - We introduce four new cocycle conjugacy invariants for $E_0$-semigroups on II$_1$ factors: a coupling index, a dimension for the gauge group, a \emph{super product system} and a $C^*$-semiflow. Using noncommutative It\^o integrals we show that the dimension of the gauge group can be computed from the structure of the \emph{additive cocycles}. We do this for the Clifford flows and even Clifford flows on the hyperfinite \twoone factor, and for the free flows on the free group factor $L(F_\infty)$. In all cases the index is $0$, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the $C^*$-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate \en-semigroups.

U2 - 10.1007/s00220-013-1790-2

DO - 10.1007/s00220-013-1790-2

M3 - Journal article

VL - 323

SP - 1155

EP - 1184

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -