Non-Cocycle-Conjugate E-Semigroups on Factors

  • Oliver T. Margetts

    Lancaster University, UK
  • R. Srinivasan

    Chennai Mathematical Institute, Siruseri, India

Abstract

We investigate E-semigroups on general factors, which are not necessarily of type I or II. We show several families on the hyperfinite II factor, which arises as tensor products, consists of mutually non-cocycle-conjugate E-semigroups. Using CCR representations associated with quasi-free states, we exhibit, for the first time, uncountable families consisting of mutually non-cocycle-conjugate E-semigroups on all type III factors, for . They are not cocycle conjugate to the E-semigroups constructed using CAR representations.

Cite this article

Oliver T. Margetts, R. Srinivasan, Non-Cocycle-Conjugate E-Semigroups on Factors. Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, pp. 299–336

DOI 10.4171/PRIMS/53-2-4