Analysis seminar

Kai-Cheong Chan, University of Waterloo

“On tensor products of digraph algebras over pre-ordered groups ”

Two natural operator algebra structures, A⊗maxB and A⊗minB, exist on the tensor product of two given unital operator algebras A and B. Because of the different properties enjoyed by the two tensor products in connection to dilation theory, it is of interest to know when they coincide. Motivated by earlier work due to Paulsen and Power, we provide conditions relating an operator algebra B and another family {Ci}i of operator algebras under which, for any operator algebra A, the equality A ⊗max B = A ⊗min B either implies, or is implied by, the equalities A ⊗max Ci = A ⊗min Ci for every i. These results can be applied to the setting of a discrete group G pre-ordered by a subsemigroup G+, where B ⊂ Cr∗(G) is the subalgebra of the reduced group C∗-algebra of G generated by G+, and Ci = A(Qi) are digraph algebras defined by considering certain pre-ordered subsets Qi of G.