Geodesic
On the noncommutative deformation of the operator graph corresponding to the Klein group
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXV, Tome 436 (2015), pp. 49-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the noncommutative operator graph $\mathcal L_\theta$ depending on a complex parameter $\theta$ recently introduced by M. E. Shirokov to construct channels with positive quantum zero-error capacity having vanishing $n$-shot capacity. We define a noncommutative group $G$ and an algebra $\mathcal A_\theta$ which is a quotient of $\mathbb CG$ with respect to a special algebraic relation depending on $\theta$ such that the matrix representation $\phi$ of $\mathcal A_\theta$ results in the algebra $\mathcal M_\theta$ generated by $\mathcal L_\theta$. In the case of $\theta=\pm1$, the representation $\phi$ degenerates into an faithful representation of $\mathbb CK_4$, where $K_4$ is the Klein group. Thus, $\mathcal L_\theta$ can be regarded as a noncommutative deformation of the graph associated with the Klein group. 
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G. G. Amosov; I. Yu. Zhdanovskiy. On the noncommutative deformation of the operator graph corresponding to the Klein group. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXV, Tome 436 (2015), pp. 49-75. http://geodesic.mathdoc.fr/item/ZNSL_2015_436_a2/

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