Dirichlet forms and symmetric markovian semigroups on ℤ 2-Graded von neumann algebras

Changsoo Bahn; Chul Ki Ko; Yong Moon Park

doi:10.1142/S0129055X03001825

Dirichlet forms and symmetric markovian semigroups on ℤ ₂-Graded von neumann algebras

Changsoo Bahn, Chul Ki Ko, Yong Moon Park

University College

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ₂-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.

Original language	English
Pages (from-to)	823-845
Number of pages	23
Journal	Reviews in Mathematical Physics
Volume	15
Issue number	8
DOIs	https://doi.org/10.1142/S0129055X03001825
Publication status	Published - 2003 Oct

Bibliographical note

Funding Information:
This work was supported by Korea Research Foundation Grant (KRF-2001-005-D20003). The authors wish to thank anonymous referees for suggesting several improvements.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1142/S0129055X03001825

Cite this

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title = "Dirichlet forms and symmetric markovian semigroups on ℤ 2-Graded von neumann algebras",

abstract = "We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.",

keywords = "CAR algebras, Dirichlet forms, Markovian semigroups, Quasi-free states, Standard forms, ℤ-graded algebras",

author = "Changsoo Bahn and Ko, {Chul Ki} and Park, {Yong Moon}",

note = "Funding Information: This work was supported by Korea Research Foundation Grant (KRF-2001-005-D20003). The authors wish to thank anonymous referees for suggesting several improvements.",

year = "2003",

month = oct,

doi = "10.1142/S0129055X03001825",

language = "English",

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TY - JOUR

T1 - Dirichlet forms and symmetric markovian semigroups on ℤ 2-Graded von neumann algebras

AU - Bahn, Changsoo

AU - Ko, Chul Ki

AU - Park, Yong Moon

N1 - Funding Information: This work was supported by Korea Research Foundation Grant (KRF-2001-005-D20003). The authors wish to thank anonymous referees for suggesting several improvements.

PY - 2003/10

Y1 - 2003/10

N2 - We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.

AB - We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.

KW - CAR algebras

KW - Dirichlet forms

KW - Markovian semigroups

KW - Quasi-free states

KW - Standard forms

KW - ℤ-graded algebras

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U2 - 10.1142/S0129055X03001825

DO - 10.1142/S0129055X03001825

M3 - Article

AN - SCOPUS:0346372603

SN - 0129-055X

VL - 15

SP - 823

EP - 845

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 8

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