Representations induced from the simplest Motzkin Cuntz–Pimsner algebra

Characterize the representations of the Cuntz algebra O_2 and the Richard Thompson groups F, T, and V obtained through the functorial lifting procedure from representations of the Cuntz–Pimsner algebra O_P of the simplest Motzkin subproduct system.

Background

The paper considers a functorial procedure that maps a pair of operators satisfying A* A + B* B = 1 to a representation of the binary Cuntz algebra O_2, whose restriction yields unitary representations of the Richard Thompson groups F, T, and V. Since the Cuntz–Pimsner algebra O_P of the simplest Motzkin subproduct system is a quotient of the Pythagorean algebra, every representation of O_P gives rise to representations of O_2 and of these Thompson groups. The paper analyzes several features of the resulting representations, including irreducibility, diffuse behavior, and special quasi-regular or monomial cases, but explicitly leaves open the general question of what representations are obtained.