1999/02/04 by C. Duval, Christian Duval, P. Lecomte +6
Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Neuroendocrine Tumor Research Advances #Quantum Algebra (math.QA) #math.DG #math.QA
paper · pdf · doi:10.48550/arxiv.math/9902032
LaTeX document, 32 pages; improved version
openalex publication_date 1999/02/04 · arxiv created 1999/02/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on T^*M and of differential operators on tensor densities over M, both viewed as modules over the Lie algebra \so(p+1,q+1) where p+q=dim(M). This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.