2000/05/01 by Ping Xu, Xu, Ping
Computer Science · Engineering · Mathematics · #Advanced Data Compression Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #graph theory and CDMA systems #math.QA #math.SG
paper · pdf · doi:10.48550/arxiv.math/0005006
LaTex, 43 pages, final version, typos corrected and references updated. Advances in Math, to appear
openalex publication_date 2000/05/01 · arxiv created 2001/07/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a general study for triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate (i.e., the corresponding Poisson manifolds are symplectic) triangular dynamical r-matrices (over \frakh^* and valued in \wedge2\frakg) are quantizable, and the quantization is classified by the relative Lie algebra cohomology H2(\frakg, \frakh)[[ℏ ]]. We also generalize this quantization method to splittable triangular dynamical r-matrices, which include all the known examples of triangular dynamical r-matrices. Finally, we arrive a conjecture that the quantization for an arbitrary triangular dynamical r-matrix is classified by the formal neighbourhood of this r-matrix in the modular space of triangular dynamical r-matrices. The dynamical r-matrix cohomology is introduced as a tool to understand such a modular space.