Abstract In this paper, we initiate the study of higher rank Baumslag–Solitar (BS) semigroups and their related C*-algebras. We focus on two rather interesting classes—one is related to products of odometers and the other is related to Furstenberg’s p, q conjecture. For the former class, whose C*-algebras are studied in 32, we here characterize the factoriality of the associated von Neumann algebras and further determine their types; for the latter, we obtain their canonical Cartan subalgebras. In the rank 1 case, we study a more general setting that encompasses (single-vertex) generalized BS semigroups. One of our main tools in this paper is from self-similar higher rank graphs and their C*-algebras.
Valente et al. (Mon,) studied this question.
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