2000/03/30 by Martin Bordemann, Bordemann, Martin
Mathematics · #16S80 #58C50 #81Q60 #81S99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.DG #math.QA #msc:16S80 #msc:58C50 #msc:81Q60 #msc:81S99
paper · pdf · doi:10.48550/arxiv.math/0003218
LATEX 2e, amssymb, latexsym, amsmath, 29 pages, Contribution to the proceedings of the Conf\erence Mosh\e Flato 1999
arxiv created 2000/03/30 · openalex publication_date 2000/03/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On every split supermanifold equipped with the Rothstein even super-Poisson bracket we construct a deformation quantization by means of a Fedosov-type procedure. In other words, the supercommutative algebra of all smooth sections of the dual Grassmann algebra bundle of an arbitrarily given vector bundle E (equipped with a fibre metric) over a symplectic manifold M will be deformed by a series of bidifferential operators having first order supercommutator proportional to the Rothstein superbracket. Moreover, we discuss two constructions related to the above result, namely the quantized BRST-cohomology for a locally free Hamiltonian Lie group action (together with H.-C.Herbig and S.Waldmann) and the classical BRST cohomology in the general coistropic (or reducible) case without using a `ghosts of ghosts' scheme (together with H.-C.Herbig).