Symplectic Reduction of Sheaves of $\mathcal{A}$-modules

Details Symplectic Reduction of Sheaves of $\mathcal{A}$-modules Symplectic Reduction of Sheaves of $\mathcal{A}$-modules

2008-02-28

arxiv.org/abs/0802.4224v1

Mathematics

Symplectic Geometry

33 pages

Scientific paper

Given an arbitrary sheaf $\mathcal{E}$ of $\mathcal{A}$-modules (or $\mathcal{A}$-module in short) on a topological space $X$, we define \textit{annihilator sheaves} of sub-$\mathcal{A}$-modules of $\mathcal{E}$ in a way similar to the classical case, and obtain thereafter the analog of the \textit{main theorem}, regarding classical annihilators in module theory, see Curtis[\cite{curtis}, pp. 240-242]. The familiar classical properties, satisfied by annihilator sheaves, allow us to set clearly the \textit{sheaf-theoretic version} of \textit{symplectic reduction}, which is the main goal in this paper.

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