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Algebras generated by reciprocals of linear forms. (English) Zbl 1049.13011
The author considers the $$K$$-algebra $$C(\Delta)$$ of rational functions generated by the set $$\{\frac{1}{\alpha}\mid \alpha\in\Delta\}$$, where $$\Delta$$ is a finite set of nonzero linear forms in several variables with coefficients in a field $$K$$ of characteristic zero. The ring $$\partial(V)$$ of differential operators with constant coefficients acts on $$C(\Delta)$$. The main result of the paper is that the standard systems of minimal generators are found and a combinatorial formula for the Poincaré series of the graded $$\partial(V)$$-module $$C(\Delta)$$ is proved.

##### MSC:
 13N10 Commutative rings of differential operators and their modules 47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
##### Keywords:
Poincaré series; algebras of differential operators
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##### References:
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