Torsion simple modules over the quantum spatial ageing algebra

Bavula, V. V.; Lü, Tao

doi:10.1080/00927872.2016.1240177

Cited by 4 publications

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References 33 publications

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“…In fact, in [5] in the tame case a classification of indecomposable generalized weight modules was obtained for a large class of algebras, the, socalled, generalized Weyl algebras (the universal enveloping algebra U (sl 2 ) and the Weyl algebras are examples of generalized Weyl algebras as well as many other quantum groups are). Recently, for some non-semisimple Lie algebras G and their quantum analogues, classifications of simple weight modules are given: the Schrödinger algebra, [15]; sl 2 ⋉ V 2 , [16], where V 2 is the simple 2dimensional sl 2 -module; the enveloping algebra of the Euclidean algebra, [14]; K q [X, Y ] ⋊ U q (sl 2 ), [17]; the quantum spatial ageing algebra, [13].…”

Section: Introductionmentioning

confidence: 99%

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

Bavula

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Futorny

2018

Proc. Amer. Math. Soc.

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For the algebra In = K x 1 , . . . , xn, ∂ 1 , . . . , ∂n, 1 , . . . , n of polynomial integrodifferential operators over a field K of characteristic zero, a classification of simple weight and generalized weight (left and right) In-modules is given. It is proven that the category of weight In-modules is semisimple. An explicit description of generalized weight In-modules is given and using it a criterion is obtained for the problem of classification of indecomposable generalized weight In-modules to be of finite representation type, tame or wild. In the tame case, a classification of indecomposable generalized weight In-modules is given. In the wild case 'natural' tame subcategories are considered with explicit description of indecomposable modules. It is proven that every generalized weight In-module is a unique sum of absolutely prime 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 shown that every indecomposable generalized weight In-module is equidimensional. A criterion is given for a generalized weight In-module to be finitely generated.

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