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The Gelfand–Naimark–Segal construction for unitary representations of $\mathbb Z_2^n$-graded Lie supergroups

Volume 113 / 2017

Mohammad Mohammadi, Hadi Salmasian Banach Center Publications 113 (2017), 263-274 MSC: 17B75; 22E45. DOI: 10.4064/bc113-0-14


We establish a Gelfand–Naimark–Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $\mathbb Z_2^n$-graded Lie supergroups.


  • Mohammad MohammadiDepartment of Mathematics
    Institute for Advanced Studies in Basic Sciences (IASBS)
    No. 444, Prof. Yousef Sobouti Blvd.
    P. O. Box 45195-1159
    Zanjan, Iran
  • Hadi SalmasianDepartment of Mathematics and Statistics
    University of Ottawa
    585 King Edward Ave
    Ottawa K1N 6N5, ON, Canada

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