Modules Over Quantum Laurent Polynomials

Gupta, Ashish

doi:10.1017/s1446788712000031

Cited by 7 publications

(2 citation statements)

References 20 publications

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“…This follows from the more general result which holds for twisted group algebras (c.f. [5,Proposition 4.3]). 3 Proof of the main theorem Theorem A.…”

Section: Gk Dimension Ore Localization and Critical Modulesmentioning

confidence: 99%

A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings

Gupta

Sarkar

2017

Algebr Represent Theor

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The Gelfand-Kirillov dimension has gained importance since its introduction as an tool in the study of non-commutative infinite dimensional algebras and their modules. In this paper we show a dichotomy for the Gelfand-Kirillov dimension of simple modules over certain simple rings of differential operators. We thus answer a question of J. C. McConnell in Representations of solvable Lie algebras V. On the Gelfand-Kirillov dimension of simple modules. J. Algebra 76 (1982), no. 2, 489-493 concerning this question for a class of algebras that arise as simple homomorphic images of solvable lie algebras. We also determine the Gelfand-Kirillov dimension of an induced module. * Corresponding author † Graduate student.

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“…This follows from the more general result which holds for twisted group algebras (c.f. [5,Proposition 4.3]). 3 Proof of the main theorem Theorem A.…”

Section: Gk Dimension Ore Localization and Critical Modulesmentioning

confidence: 99%

A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings

Gupta

Sarkar

2017

Algebr Represent Theor

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“…Lemma 3.1 (Lemma 4.1 of [7]). Suppose that F * A has a finitely generated module M and A has a subgroup C with A/C torsion-free, rk(C) = G K -dim(M ), and F * C commutative.…”

Section: The Gk Dimension Of An F * A-modulementioning

confidence: 99%

Representations of then-Dimensional Quantum Torus

Gupta

2016

Communications in Algebra

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The n-dimensional quantum torus O q F × n is defined as the associative F -algebra generated by x 1x n together with their inverses satisfying the relations x i x j = q ij x j x i , where q = q ij . We show that the modules that are finitely generated over certain commutative sub-algebras B are B-torsion-free and have finite length. We determine the Gelfand-Kirillov dimensions of simple modules in the case when dim stands for the Krull dimension. In this case, if M is a simplewhere Z C stands for the center of an algebra C. We also show that there always exists a simple F * A-module satisfying the above inequality.

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The q-Onsager algebra and the quantum torus

Goff

2024

Journal of Combinatorial Theory, Series A

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Modules Over Quantum Laurent Polynomials

Cited by 7 publications

References 20 publications

A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings

A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings

Representations of then-Dimensional Quantum Torus

The q-Onsager algebra and the quantum torus

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