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, G (2019). On operator systems generated by reducible projective unitary representations of compact groups. Turkish Journal of Mathematics 43 (5): 2366-2370. https://doi.org/10.3906/mat-1906-59
