Modules over algebras related to the Virasoro algebra

2015 ◽  
Vol 26 (09) ◽  
pp. 1550070 ◽  
Author(s):  
Qiufan Chen ◽  
Yan-an Cai
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Virasoro Algebra ◽  
Schrödinger Algebra ◽  
Weight Modules

In this paper, we consider a class of non-weight modules for some algebras related to the Virasoro algebra: The algebra Vir (a, b), the twisted deformative Schrödinger–Virasoro Lie algebras and the Schrödinger algebra. We study the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank 1 for these algebras. Moreover, the simplicities of these modules are determined.

scholarly journals Non-weight modules over the Heisenberg–Virasoro algebra and the W algebra W(2,2)

2017 ◽  
Vol 16 (05) ◽  
pp. 1750097 ◽  
Author(s):  
Hongjia Chen ◽  
Xiangqian Guo
Keyword(s):  
Cartan Subalgebra ◽  
Virasoro Algebra ◽  
Interesting Case ◽  
Universal Enveloping Algebra ◽  
Simple Modules ◽  
Enveloping Algebra ◽  
Weight Modules

In this paper, we construct and study some non-weight modules for the Heisenberg–Virasoro algebra and the [Formula: see text] algebra [Formula: see text]. We determine the modules, whose restriction to the universal enveloping algebra of the degree-[Formula: see text] part (modulo center) are free of rank [Formula: see text] for these two algebras. In the most interesting case, this degree-[Formula: see text] part is not the Cartan subalgebra. We also determine the simplicity of these modules, which provide new simple modules for the [Formula: see text] algebra [Formula: see text].

scholarly journals N-Derivations for Finitely Generated Graded Lie Algebras

2016 ◽  
Vol 23 (02) ◽  
pp. 205-212
Author(s):  
Haifeng Lian ◽  
Cui Chen
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Virasoro Algebra ◽  
Natural Generalization ◽  
Finitely Generated ◽  
Moody Algebra ◽  
Graded Lie Algebras ◽  
Derivation Algebra ◽  
Finite Dimensional ◽  
Lie Derivation

The N-derivation is a natural generalization of derivation and triple derivation. Let [Formula: see text] be a finitely generated Lie algebra graded by a finite-dimensional Cartan subalgebra. In this paper, a sufficient condition for the Lie N-derivation algebra of [Formula: see text] coinciding with the Lie derivation algebra of [Formula: see text] is given. As applications, any N-derivation of the Schrödinger-Virasoro algebra, generalized Witt algebra, Kac-Moody algebra or their Borel subalgebra is a derivation.

scholarly journals Characterization of Simple Highest Weight Modules

2013 ◽  
Vol 56 (3) ◽  
pp. 606-614 ◽  
Author(s):  
Volodymyr Mazorchuk ◽  
Kaiming Zhao
Keyword(s):  
Lie Algebras ◽  
Positive Root ◽  
Virasoro Algebra ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Heisenberg Algebras ◽  
Higher Rank ◽  
Highest Weight Modules ◽  
Weight Modules

Abstract.We prove that for simple complex finite dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, and the Heisenberg–Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro algebras and for Heisenberg algebras.

scholarly journals SIMPLE BOUNDED WEIGHT MODULES OF $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right),\kern0.5em \mathfrak{sp}\left(\infty \right) $$

2020 ◽  
Vol 25 (4) ◽  
pp. 1125-1160
Author(s):  
DIMITAR GRANTCHAROV ◽  
IVAN PENKOV
Keyword(s):  
Lie Algebras ◽  
Weight Modules

Abstract We classify the simple bounded weight modules of the Lie algebras $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right) $$ sl ∞ , o ∞ and $$ \mathfrak{sp}\left(\infty \right) $$ sp ∞ , and compute their annihilators in $$ U\left(\mathfrak{sl}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{o}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{sp}\left(\infty \right)\right) $$ U sl ∞ , U o ∞ , U sp ∞ , respectively.

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