On Linear Structure of Non-commutative Operator Graphs


We continue the study of non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary actions of the circle group and the Heisenber-Weyl group as well. It is shown that the graphs generated by the circle group has the system of unitary generators fulfilling permutations of basis vectors. For the graph generated by the Heisenberg-Weyl group the explicit formula for a dimension is given. Thus, we found a new description of the linear structure for the operator graphs introduced in our previous works.

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The work is supported by Russian Science Foundation under the grant no. 19-11-00086.

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Correspondence to G. G. Amosov or A. S. Mokeev.

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Submitted by S. A. Grigoryan

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Amosov, G.G., Mokeev, A.S. On Linear Structure of Non-commutative Operator Graphs. Lobachevskii J Math 40, 1440–1443 (2019). https://doi.org/10.1134/S1995080219100032

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Keywords and phrases

  • non-commutative operator graphs
  • covariant resolution of identity
  • quantum anticliques