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Regular version of the site

Article

On the algebra generated by projectors with commutator relation

Lobachevskii Journal of Mathematics. 2017. Vol. 38. No. 4. P. 670-687.
Zhdanovskiy I., Kocherova A. S.

In this article we apply methods of representation theory and combinatorial algebra to the different problems related to quantum tomography. For this purpose, we introduce the algebra generated by projectors satisfying some commutator relation. In this paper we study this commutator relation by combinatorialmethods and develop the representation theory of this algebra. Also, we apply our results to the case of mutually unbiased bases in dimension 7.