Torsion theories induced from commutative subalgebras.

DOI10.1016/j.jpaa.2011.04.014zbMath1236.16006arXiv1003.2332OpenAlexW2964080982MaRDI QIDQ649861

Manuel Saorín, Vyacheslav M. Futorny, Sergiy Ovsienko

Publication date: 6 December 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2332

zbMATH Keywords

torsion theoriesuniversal enveloping algebrasrepresentationssimple modulesassociated prime idealsfinitely generated subalgebrascoheights of prime idealsHarish-Chandra subalgebrasstratifications of categories of modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Module categories in associative algebras (16D90) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Infinite-dimensional Lie (super)algebras (17B65) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (7)

Simple \(\mathfrak{sl} (V)\)-modules which are free over an abelian subalgebra ⋮ Twisting functors and Gelfand–Tsetlin modules over semisimple Lie algebras ⋮ New families of irreducible weight modules over \(\mathfrak{sl}_3\) ⋮ Generalized Verma modules over \(\mathfrak{sl}_{n + 2}\) induced from \(\mathcal{U}(\mathfrak{h}_n)\)-free \(\mathfrak{sl}_{n + 1}\)-modules ⋮ Geometric construction of Gelfand-Tsetlin modules over simple Lie algebras ⋮ Simple \(\mathfrak{sl}_{n + 1}\)-module structures on \(\mathcal{U}(\mathfrak{h})\) ⋮ Representations of Lie algebras

Cites Work

• Shifted Yangians and finite \(W\)-algebras
• Galois orders in skew monoid rings.
• The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
• Simple modules of the Witten-Woronowicz algebra.
• Infinite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) related to complex analogs of the Gelfand-Tsetlin patterns and general hypergeometric functions on the Lie group \(\text{GL}(n,\mathbb C)\).
• Classification of irreducible weight modules
• The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite \(W\)-algebras
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• ON CERTAIN COMMUTATIVE SUBALGEBRAS OF A UNIVERSAL ENVELOPING ALGEBRA
• Lie Algebra Modules with Finite Dimensional Weight Spaces, I
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