{"title":"Remarks on CCR and CAR flows over closed convex cones","authors":"Anbu Arjunan","doi":"10.1142/s0219025721500211","DOIUrl":null,"url":null,"abstract":"For a closed convex cone <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> in <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> which is spanning and pointed, i.e. <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">−</mml:mo> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">∩</mml:mo><mml:mo stretchy=\"false\">−</mml:mo><mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">}</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> we consider a family of <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>-semigroups over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> consisting of a certain family of CCR flows and CAR flows over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> and classify them up to the cocycle conjugacy.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219025721500211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For a closed convex cone P in ℝd which is spanning and pointed, i.e. P−P=ℝd and P∩−P={0}, we consider a family of E0-semigroups over P consisting of a certain family of CCR flows and CAR flows over P and classify them up to the cocycle conjugacy.
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