Hilbert series of modules over Lie algebroids

Details Hilbert series of modules over Lie algebroids Hilbert series of modules over Lie algebroids

2011-06-27

arxiv.org/abs/1106.5395v4

Mathematics

Commutative Algebra

36 pages. This is a substantial revision of the previous version

Scientific paper

We consider modules $M$ over Lie algebroids $\g_A$ which are of finite type over a local noetherian ring $A$. Using ideals $J\subset A$ such that $\g_A \cdot J\subset J $ and the length $\ell_{\g_A}(M/JM)< \infty$ we can define in a natural way theHilbert series of $M$ with respect to the defining ideal $J$. This notion is in particular studied for modules over the Lie algebroid of $k$-linear derivations $\g_A=T_A(I)$ that preserve an ideal $I\subset A$, for example when $A=\Oc_n$, the ring of convergent power series.

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