Ukrainian Mathematical Journal

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

Representations of canonical anticommutation relations with orthogonality condition

  • R. Ya. Yakymiv
Article
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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 \(a_j^{2}\ne 0 \).

Keywords

Irreducible Representation Orthonormal Basis Orthogonality Condition Polar Decomposition Partial Isometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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