2020/06/24 by Deaconu, Valentin
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2006.14106
We introduce certain C^*-algebras and k-graphs associated to k finite dimensional unitary representations ρ1,...,ρk of a compact group G. We define a higher rank Doplicher-Roberts algebra Oρ1,...,ρk, constructed from intertwiners of tensor powers of these representations. Under certain conditions, we show that this C^*-algebra is isomorphic to a corner in the C^*-algebra of a row finite rank k graph Λ with no sources. For G finite and ρi faithful of dimension at least 2, this graph is irreducible, it has vertices G and the edges are determined by k commuting matrices obtained from the character table of the group. We illustrate with some examples when Oρ1,...,ρk is simple and purely infinite, and with some K-theory computations.