scholarly journals Classification of irreducible bounded weight modules over the derivation Lie algebras of quantum tori

2016 ◽  
Vol 495 ◽  
pp. 11-23
Author(s):  
Genqiang Liu ◽  
Kaiming Zhao
Keyword(s):  
Lie Algebras ◽  
Quantum Tori ◽  
Weight Modules

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 Quantum Tori with Involution

2002 ◽  
Vol 45 (4) ◽  
pp. 711-731 ◽  
Author(s):  
Yoji Yoshii
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Type A ◽  
Affine Lie Algebras ◽  
Precise Information ◽  
Quantum Tori ◽  
Type C

AbstractQuantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type C.

scholarly journals Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A)=3

2016 ◽  
Vol 110 ◽  
pp. 25-29 ◽  
Author(s):  
Hamid Darabi ◽  
Farshid Saeedi ◽  
Mehdi Eshrati
Keyword(s):  
Lie Algebras

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

Complete classification of pseudo H-type Lie algebras: I

2017 ◽  
Vol 190 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Kenro Furutani ◽  
Irina Markina
Keyword(s):  
Lie Algebras ◽  
Complete Classification

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.

scholarly journals Classification of irreducible weight modules

2000 ◽  
Vol 50 (2) ◽  
pp. 537-592 ◽  
Author(s):  
Olivier Mathieu
Keyword(s):  
Weight Modules
Sign in / Sign up

Export Citation Format

Share Document