SIMPLE INFINITE DIMENSIONAL QUOTIENTS OF C~*(G) FOR DISCRETE 5-DIMENSIONAL NILPOTENT GROUPS G

摘要

In each of 3 and 4 dimensions there is a unique (up to isomorphism) connected, simply connected, nilpotent Lie group, which we call G_3 and G_4, respectively (following Nielsen). In [10] we showed that the simple C~*-algebras A_θ~4 arising from Anzai flows (with irrational θ), which had been studied in [7], [12], and [20], are iso-morphic to simple infinite dimensional quotients of C~*(H_4), where H_4 is the lattice subgroup of G_4, in the same way that the irrational rotation algebras A_θ~3 (as we call them to conform with our other notation) are isomorphic to such quotients of C~* (H_3), where H_3 is the lattice subgroup of the Heisenberg group G_3. Also determined in [10; Theorem 2] were crossed product presentations of the A_θ~4's. The 5-dimensional case, which is studied in the present paper, is immediately complicated by the existence of 6 (non-isomorphic) connected and simply connected, nilpotent, Lie groups G_(5,i), 1 ≤ i ≤ 6 (see [11]). Following the Preliminaries, a section is devoted to each of these groups.