Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators. (English) Zbl 1431.16022
Summary: For the algebra \( \mathbb{I}_1= K\langle x, \frac {d}{dx}, \int \rangle \) of polynomial integro-differential operators over a field \( K\) of characteristic zero, a classification of indecomposable, generalized weight \( \mathbb{I}_1\)-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules; it is proven that they are finite dimensional vector spaces.
MSC:
| 16S32 | Rings of differential operators (associative algebraic aspects) |
| 16G99 | Representation theory of associative rings and algebras |
Keywords:
algebra of polynomial integro-differential operators; generalized weight module; indecomposable module; simple moduleReferences:
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