Lectures on Sl <sub>2</sub> (C)-Modules

Mazorchuk, Volodymyr

doi:10.1142/p695

Cited by 60 publications

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“…If N is a simple c-module on which l 2 acts injectively, then N localizes to a simple A-module N ′ . As A is finitely generated (it is generated by l 0 , l 1 , l 2 and l 2 must act as some scalar, say λ ∈ C \ {0}, on N ′ (confer the proof of [Mz,Theorem 4.7]). This means that l 2 1 − λl 2 annihilates N. Again, it follows that the restriction L of N to b is simple and N ∼ = ϕ µ (L), where µ = λ −1 .…”

Section: Old and New Simple Virasoro Modulesmentioning

confidence: 99%

Simple Virasoro modules which are locally finite over a positive part

Mazorchuk

Zhao

2013

Sel. Math. New Ser.

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117

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Abstract. We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This reduces the problem of classification of simple Virasoro modules which are locally finite over a positive part to classification of simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras all simple modules are classified by R. Block and we extend this classification to the next member of the family. As a result we recover many known but also construct a lot of new simple Virasoro modules. We also propose a revision of the setup for study of Whittaker modules.

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Section: Old and New Simple Virasoro Modulesmentioning

confidence: 99%

Simple Virasoro modules which are locally finite over a positive part

Mazorchuk

Zhao

2013

Sel. Math. New Ser.

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117

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“…Simple weight modules with finite-dimensional weight spaces (sometimes also called Harish-Chandra modules) are classified for several classes of algebras, including simple finite-dimensional algebras ( [M2]) and various generalized Virasoro algebras ([M1,Ma3,LZ]). In the general case, however, the problem is solved only for the Lie algebra sl 2 ( [Ga], see [Ma5,Chapter 3] …”

Section: Introductionmentioning

confidence: 99%

Supports of weight modules over Witt algebras

Mazorchuk

Zhao

2011

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Abstract. In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras W n , we explicitly describe supports of such modules. We also obtain some descriptions on the support of an arbitrary simple weight module over a Z n -graded Lie algebra g having a root space decomposition ⊕ α∈Z n g α with respect to the abelian subalgebra g 0 , with the property [g α , g β ] = g α+β for all α, β ∈ Z n , α ̸ = β (this class contains the algebra W n ).

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“…In this subsection we introduce one of the prototypical examples for quasi-hereditary algebras, blocks of Bernstein-GelfandGelfand category O. For a general introduction to BGG category O the reader can consult [42], or (for the sl 2 -case) [69].…”

Section: Quasi-hereditary Algebrasmentioning

confidence: 99%

In the bocs seat: Quasi-hereditary algebras and representation type

Külshammer

2017

Representation Theory – Current Trends and Perspectives

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Abstract. This paper surveys bocses, quasi-hereditary algebras and their relationship which was established in a recent result by Koenig, Ovsienko, and the author. Particular emphasis is placed on applications of this result to the representation type of the category filtered by standard modules for a quasi-hereditary algebra. In this direction, joint work with Thiel is presented showing that the subcategory of modules filtered by Weyl modules for tame Schur algebras is of finite representation type. The paper also includes a new proof for the classification of quasi-hereditary algebras with two simple modules, a result originally obtained by .

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Lectures on Sl ₂ (C)-Modules

Abstract: Lectures on Sl2(C)-Modules Downloaded from www.worldscientific.com by 44.224.250.200 on 12/20/20. Re-use and distribution is strictly not permitted, except for Open Access articles.

Cited by 60 publications

References 0 publications

Simple Virasoro modules which are locally finite over a positive part

Simple Virasoro modules which are locally finite over a positive part

Supports of weight modules over Witt algebras

In the bocs seat: Quasi-hereditary algebras and representation type

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Lectures on Sl 2 (C)-Modules

Abstract: Lectures on Sl2(C)-Modules Downloaded from www.worldscientific.com by 44.224.250.200 on 12/20/20. Re-use and distribution is strictly not permitted, except for Open Access articles.

Cited by 60 publications

References 0 publications

Simple Virasoro modules which are locally finite over a positive part

Simple Virasoro modules which are locally finite over a positive part

Supports of weight modules over Witt algebras

In the bocs seat: Quasi-hereditary algebras and representation type

Contact Info

Product

Resources

About

Lectures on Sl ₂ (C)-Modules