IRREDUCIBLE MODULES OVER THE E6-TYPE LIE ALGEBRA

2007 ◽  
Vol 29 (2) ◽  
pp. 269-277
Author(s):  
Yang-Gon Kim
Keyword(s):  
Lie Algebra ◽  
Irreducible Modules

scholarly journals A Note on the Rank of a Restricted Lie Algebra

2018 ◽  
Vol 25 (04) ◽  
pp. 653-660
Author(s):  
Hao Chang
Keyword(s):  
Lie Algebra ◽  
Short Note ◽  
Restricted Lie Algebra ◽  
Irreducible Modules ◽  
Contact Algebra

In this short note, we study the rank of a restricted Lie algebra (𝔤, [p]), and give some applications which concern the dimensions of non-trivial irreducible modules. We also compute the rank of the restricted contact algebra.

On basic Cycles of An, Bn, Cn and Dn

1985 ◽  
Vol 37 (1) ◽  
pp. 122-140 ◽  
Author(s):  
D. J. Britten ◽  
F. W. Lemire
Keyword(s):  
Lie Algebra ◽  
Dual Space ◽  
Cartan Subalgebra ◽  
Closed Field ◽  
Generating Set ◽  
Enveloping Algebra ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Positive Roots

In this paper, we investigate a conjecture of Dixmier [2] on the structure of basic cycles. Our interest in basic cycles arises primarily from the fact that the irreducible modules of a simple Lie algebra L having a weight space decomposition are completely determined by the irreducible modules of the cycle subalgebra of L. The basic cycles form a generating set for the cycle subalgebra.First some notation: F denotes an algebraically closed field of characteristic 0, L a finite dimensional simple Lie algebra of rank n over F, H a fixed Cartan subalgebra, U(L) the universal enveloping algebra of L, C(L) the centralizer of H in U(L), Φ the set of nonzero roots in H*, the dual space of H, Δ = {α1, …, αn} a base of Φ, and Φ+ = {β1, …, βm} the positive roots corresponding to Δ.

scholarly journals Maximal finite abelian subgroups of E8

2017 ◽  
Vol 147 (5) ◽  
pp. 993-1008 ◽  
Author(s):  
Cristina Draper ◽  
Alberto Elduque
Keyword(s):  
Algebraic Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Homogeneous Component ◽  
Closed Field ◽  
Simple Algebraic Group ◽  
Algebraically Closed Field ◽  
Irreducible Modules ◽  
Abelian Subgroups

The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the simple Lie algebra of type E8 with trivial neutral homogeneous component. The Brauer invariant of the irreducible modules for graded semisimple Lie algebras plays a key role.

Cohomology of Lie Conformal Algebra Vir⋉Cur g

2021 ◽  
Vol 28 (03) ◽  
pp. 507-520
Author(s):  
Maosen Xu ◽  
Yan Tan ◽  
Zhixiang Wu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Irreducible Modules

In this article, we compute cohomology groups of the semisimple Lie conformal algebra [Formula: see text] with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra [Formula: see text].

FEIGIN-FUCHS REPRESENTATIONS OF $A ^{(1)} _n$ AFFINE LIE ALGEBRA AND THE ASSOCIATED PARAFERMIONIC ALGEBRA

1990 ◽  
Vol 05 (03) ◽  
pp. 215-224 ◽  
Author(s):  
KATSUSHI ITO ◽  
YOICHI KAZAMA
Keyword(s):  
Lie Algebra ◽  
Affine Lie Algebra ◽  
Irreducible Modules

Feigin-Fuchs representations of [Formula: see text] affine Lie algebra and the associated parafermionic algebra are obtained. The screening charges, essential for analyzing the structure of irreducible modules, are also discussed.

scholarly journals Jet modules for the centerless Virasoro-like algebra

2019 ◽  
Vol 18 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Xiangqian Guo ◽  
Genqiang Liu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Block Type ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Infinite Dimensional Lie Algebra ◽  
Area Preserving

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a [Formula: see text]-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over [Formula: see text]. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of [Irreducible representations for toroidal Lie algebras, J. Algebras 221 (1999) 188–231; Weight modules over exp-polynomial Lie algebras, J. Pure Appl. Algebra 191 (2004) 23–42]. Consequently, indecomposable jet modules are described using modules over the algebra [Formula: see text], which is the “positive part” of a Block type algebra studied first by [Some infinite-dimensional simple Lie algebras in characteristic [Formula: see text] related to those of Block, J. Pure Appl. Algebra 127(2) (1998) 153–165] and recently by [A [Formula: see text]-graded generalization of the Witt-algebra, preprint; Classification of simple Lie algebras on a lattice, Proc. London Math. Soc. 106(3) (2013) 508–564]).

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