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Representations of canonical anticommutation relations with orthogonality condition

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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 \(a_j^{2}\ne 0 \).

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Author information

Correspondence to R. Ya. Yakymiv.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1266–1272, September, 2012.

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Yakymiv, R.Y. Representations of canonical anticommutation relations with orthogonality condition. Ukr Math J 64, 1440–1447 (2013). https://doi.org/10.1007/s11253-013-0726-5

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Keywords

  • Irreducible Representation
  • Orthonormal Basis
  • Orthogonality Condition
  • Polar Decomposition
  • Partial Isometry