Ukrainian Mathematical Journal

, Volume 64, Issue 9, pp 1440–1447 | Cite as

Representations of canonical anticommutation relations with orthogonality condition

  • R. Ya. Yakymiv
We study a class of *-representations of the *-algebra \( A_0^{(d) } \) generated by relations of the form
$$ A_0^{(d) }=\mathbb{C}\langle{{a_j},a_j^{*}} |a_j^{*}{a_j}=1-{a_j}a_j^{*},a_i^{*}{a_j}=0,\;i\ne j,\;i\;j=1,\ldots,d\rangle $$
and propose a description of the classes of unitary equivalence of irreducible *-representations of \( A_0^{(d) } \) such that there exists j = 1, … , d for which \(a_j^{2}\ne 0 \).


Irreducible Representation Orthonormal Basis Orthogonality Condition Polar Decomposition Partial Isometry 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • R. Ya. Yakymiv
    • 1
  1. 1.National University of Biological Resources and Nature Management of UkraineKyivUkraine

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