2017
Том 69
№ 9

# Representations of canonical anticommutation relations with orthogonality condition

Yakymiv R. Ya.

Abstract

We study the class of Hilbert space representations of the ∗-algebra $A^{(d)}_0$ generated by relations of the form $$A^{(d)}_0 = \mathbb{C}\langle a_j, a_j^{*} | a_j^{*} a_j = 1 - a_j a_j^{*},\; a_j, a_j^{*} = 0, i \neq j,\; i, j = 1,...,d\rangle,$$ Namely, we describe the classes of unitary equivalence of irreducible representations of $A^{(d)}_0$ such that there exists $j = 1,...,d$ for which $a^2_j \neq 0$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 9, pp 1440-1447.

Citation Example: Yakymiv R. Ya. Representations of canonical anticommutation relations with orthogonality condition // Ukr. Mat. Zh. - 2012. - 64, № 9. - pp. 1266-1272.

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