Operator systems from discrete groups

Understand

We formulate a general framework for the study of operator systems arising from discrete groups.

• We study in detail the operator system of the free group on $n$ generators, as well as the operator systems of the free products of finitely many copies of the two-element group $\mathbb Z_2$.
• We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products.
• We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.