TY - JOUR

T1 - On Linear Structure of Non-commutative Operator Graphs

AU - Amosov, G. G.

AU - Mokeev, A. S.

N1 - Amosov, G.G., Mokeev, A.S. On Linear Structure of Non-commutative Operator Graphs. Lobachevskii J Math 40, 1440–1443 (2019) doi:10.1134/S1995080219100032

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - covariant resolution of identity

KW - non-commutative operator graphs

KW - quantum anticliques

UR - http://www.scopus.com/inward/record.url?scp=85073500548&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/linear-structure-noncommutative-operator-graphs

U2 - 10.1134/S1995080219100032

DO - 10.1134/S1995080219100032

M3 - Article

AN - SCOPUS:85073500548

VL - 40

SP - 1440

EP - 1443

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 10

ER -