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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)
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