| Full text | |
| Author(s): |
V. Bavula, V.
;
Bekkert, V.
;
Futorny, V.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ASIAN JOURNAL OF MATHEMATICS; v. 25, n. 5, p. 30-pg., 2021-10-01. |
| Abstract | |
For the algebra IIn = K < x(1),..., x(n),partial derivative(1),...,partial derivative(n), integral(1),..., integral(n)> of polynomial integrodifferential operators over a field K of characteristic zero, a classification of simple weight and generalized weight (left and right) IIn-modules is given. It is proven that the category of weight IIn-modules is semisimple. An explicit description of generalized weight IIn-modules is given and using it a criterion is obtained for the problem of classification of indecomposable generalized weight IIn-modules to be of finite representation type, tame or wild. In the tame case, a classification of indecomposable generalized weight IIn-modules is given. In the wild case 'natural' tame subcategories are considered with explicit description of indecomposable modules. For an arbitrary ring R, we introduce the concept of absolutely prime R-module (a nonzero R-module M is absolutely prime if all nonzero subfactors of M have the same annihilator). It is proven that every generalized weight IIn-module is a unique sum of absolutely prime modules. It is also shown that every indecomposable generalized weight IIn-module is equidimensional. A criterion is given for a generalized weight IIn-module to be finitely generated. (AU) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/02946-0 - Polynomial integro-differential operators and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |