Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators

Bavula, V.; Bekkert, V.; Futorny, V.

doi:10.1090/proc/13985

Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators
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by V. Bavula, V. Bekkert and V. Futorny PDF

Proc. Amer. Math. Soc. 146 (2018), 2373-2380 Request permission

Abstract:

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.

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