Turkish Journal of Mathematics
Abstract
We study reducible projective unitary representations $(U_g)_{g\in G}$ of a compact group $G$ in separable Hilbert spaces $H$. It is shown that there exist the projections $Q$ and $P$ for which ${\mathcal V}=\overline {span(U_gQU_g^*,\ g\in G)}$ is the operator system and $P{\mathcal V}P=\{{\mathbb C}P\}$. As an example, a bipartite Hilbert space $H={\mathfrak {H}}\otimes {\mathfrak {H}}$ is considered. In this case, the action of $(U_g)_{g\in G}$ has the property of transforming separable vectors to entangled.
DOI
10.3906/mat-1906-59
Keywords
Operator systems, covariant resolutions of identity, reducible unitary representations of compact groups, quantum anticliques
First Page
2366
Last Page
2370
Recommended Citation
AMOSOV, GRIGORI
(2019)
"On operator systems generated by reducible projective unitary representations of compact groups,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 23.
https://doi.org/10.3906/mat-1906-59
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/23
