The inner structure of boundary quotients of right LCM semigroups
We study distinguished subalgebras and automorphisms of boundary quotients arising from algebraic dynamical systems (G, P, θ). Our work includes a complete solution to the problem of extending Bogolubov automorphisms from the Cuntz algebra in 2 ≤ p < ∞ generators to the p-adic ring C∗algebra. For the case where P is abelian and C∗(G) is a maximal abelian subalgebra, we establish a picture for the automorphisms of the boundary quotient that fix C∗(G) pointwise. This allows us to show that they form a maximal abelian subgroup of the entire automorphism group.