For any number h such that h := h/2 pi is irrational and any skew-symmetric, non-degenerate bilinear form sigma : Z(2g) x Z(2g) -> Z, let be A(g,sigma)(h) be the twisted group *-algebra C[Z(2g)] and consider the ergodic group of *-automorphisms of A(g,sigma)(h) induced by the action of the symplectic group Sp (Z(2g), sigma). We show that the only Sp (Z(2g),sigma)-invariant state on A(g,sigma)(h) is the trace state tau.
Invariant States on Noncommutative Tori
Bambozzi, F;
2021
Abstract
For any number h such that h := h/2 pi is irrational and any skew-symmetric, non-degenerate bilinear form sigma : Z(2g) x Z(2g) -> Z, let be A(g,sigma)(h) be the twisted group *-algebra C[Z(2g)] and consider the ergodic group of *-automorphisms of A(g,sigma)(h) induced by the action of the symplectic group Sp (Z(2g), sigma). We show that the only Sp (Z(2g),sigma)-invariant state on A(g,sigma)(h) is the trace state tau.
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