The torus quantization conjecture for infinite-dimensional basic algebras

Let $M$ be a symplectic manifold and ${\mathfrak b}$ a basic algebra such that $P^1({\mathfrak b})$ is dense in $C^{\infty}(M)$, where $P^1({\mathfrak b})$ denotes the polynomial algebra with constants included. Torus quantization conjecture. There exists a nontrivial quantization of $(C^{\infty}(M),{\mathfrak b})$. This proposal concerns the exceptional infinite-dimensional case, exemplified by the torus, where the basic algebra consists of mean-zero trigonometric polynomials and the irreducibility requirement does not produce an obstruction. The source gives no general proof or resolution.