An infinitesimal-birational duality through differential operators

2005/11/30 by Tomasz Maszczyk, Maszczyk, Tomasz
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AG #math.QA #msc:16S30 #msc:16S32

paper · pdf · doi:10.48550/arxiv.math/0511720

18 pages

arxiv created 2005/11/30 · arxiv updated 2009/12/01

Abstract

The structure of filtered algebras of Grothendieck's differential operators of truncated polynomials in one variable and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.

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