scholarly journals Classification of irreducible integrable modules for twisted toroidal Lie algebras with finite-dimensional weight spaces

2008 ◽  
Vol 237 (1) ◽  
pp. 151-181 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Integrable Modules

scholarly journals k-step nilpotent Lie algebras

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Deformation Process ◽  
Nilpotent Lie Algebras ◽  
Early Stages ◽  
Finite Dimensional ◽  
Contraction Process ◽  
Finite Dimensional Lie Algebras

AbstractThe classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this problem. We determine families for some fixed invariants and the classification follows by a deformation process or a contraction process. We focus on the case of 2- and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid with respect to this cohomology. Other

scholarly journals Classification of irreducible integrable highest weight modules for current Kac–Moody algebras

2016 ◽  
Vol 16 (07) ◽  
pp. 1750123 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Direct Sums ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Highest Weight Modules ◽  
Weight Modules

This paper classifies irreducible, integrable highest weight modules for “current Kac–Moody Algebras” with finite-dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac–Moody Lie algebras.

scholarly journals Classification of linked indecomposable modules of a family of solvable Lie algebras over an arbitrary field of characteristic 0

2015 ◽  
Vol 15 (02) ◽  
pp. 1650029 ◽  
Author(s):  
Leandro Cagliero ◽  
Fernando Szechtman
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Weight Space ◽  
Arbitrary Field ◽  
Nilpotent Radical ◽  
Indecomposable Modules ◽  
Finite Dimensional ◽  
A Chain ◽  
Algebra Over A Field

Let 𝔤 be a finite-dimensional Lie algebra over a field of characteristic 0, with solvable radical 𝔯 and nilpotent radical 𝔫 = [𝔤, 𝔯]. Given a finite-dimensional 𝔤-module U, its nilpotency series 0 ⊂ U(1) ⊂ ⋯ ⊂ U(m) = U is defined so that U(1) is the 0-weight space of 𝔫 in U, U(2)/U(1) is the 0-weight space of 𝔫 in U/U(1), and so on. We say that U is linked if each factor of its nilpotency series is a uniserial 𝔤/𝔫-module, i.e. its 𝔤/𝔫-submodules form a chain. Every uniserial 𝔤-module is linked, every linked 𝔤-module is indecomposable with irreducible socle, and both converses fail. In this paper, we classify all linked 𝔤-modules when 𝔤 = 〈x〉 ⋉ 𝔞 and ad x acts diagonalizably on the abelian Lie algebra 𝔞. Moreover, we identify and classify all uniserial 𝔤-modules amongst them.

Integrable Representations for Twisted Generalized Virasoro-Toroidal Lie Algebras

2008 ◽  
Vol 15 (03) ◽  
pp. 415-430
Author(s):  
Jiayuan Fu ◽  
Cuipo Jiang ◽  
Yucai Su
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Integrable Modules

In this paper, we classify irreducible integrable modules of twisted generalized Virasoro-toroidal Lie algebras τ with finite-dimensional weight spaces.

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