Group Gradings on Lie Algebras and Applications to Geometry: II

2014 ◽  
pp. 1-40 ◽  
Author(s):  
Yuri Bahturin ◽  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebras ◽  
Group Gradings

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

scholarly journals Arithmetically-free group-gradings of Lie algebras: II

2017 ◽  
Vol 492 ◽  
pp. 457-474 ◽  
Author(s):  
Wolfgang Alexander Moens
Keyword(s):  
Lie Algebras ◽  
Free Group ◽  
Group Gradings

scholarly journals Group gradings on restricted Cartan-type Lie algebras

2011 ◽  
Vol 253 (2) ◽  
pp. 289-319
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov
Keyword(s):  
Lie Algebras ◽  
Cartan Type ◽  
Group Gradings

scholarly journals Group Gradings on Finite Dimensional Lie Algebras

2013 ◽  
Vol 20 (04) ◽  
pp. 573-578 ◽  
Author(s):  
Dušan Pagon ◽  
Dušan Repovš ◽  
Mikhail Zaicev
Keyword(s):  
Finite Group ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Solvable Radical ◽  
Finite Dimensional ◽  
Levi Subalgebra ◽  
Group Gradings ◽  
Finite Dimensional Lie Algebras

We study gradings by non-commutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if L is graded by a non-abelian finite group G, then the solvable radical R of L is G-graded and there exists a Levi subalgebra B=H1⊕ ⋯ ⊕ Hm homogeneous in G-grading with graded simple summands H1,…,Hm. All Supp Hi (i=1,…,m) are commutative subsets of G.

scholarly journals Group Gradings on Filiform Lie Algebras

2015 ◽  
Vol 44 (1) ◽  
pp. 40-62 ◽  
Author(s):  
Yuri Bahturin ◽  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebras ◽  
Group Gradings ◽  
Filiform Lie Algebras

Multiplicity-Free Gradings on Semisimple Lie and Jordan Algebras and Skew Root Systems

2019 ◽  
Vol 26 (01) ◽  
pp. 123-138
Author(s):  
Gang Han ◽  
Yucheng Liu ◽  
Kang Lu
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Root Systems ◽  
Jordan Algebras ◽  
Homogeneous Component ◽  
New Approach ◽  
Jordan Type ◽  
Semisimple Lie Algebras ◽  
Group Gradings ◽  
Multiplicity Free

A G-grading on an algebra, where G is an abelian group, is called multiplicity-free if each homogeneous component of the grading is 1-dimensional. We introduce skew root systems of Lie type and skew root systems of Jordan type, and use them to construct multiplicity-free gradings on semisimple Lie algebras and on semisimple Jordan algebras respectively. Under certain conditions the corresponding Lie (resp., Jordan) algebras are simple. Two families of skew root systems of Lie type (resp., of Jordan type) are constructed and the corresponding Lie (resp., Jordan) algebras are identified. This is a new approach to study abelian group gradings on Lie and Jordan algebras.

scholarly journals Group gradings on simple Lie algebras in positive characteristic

2008 ◽  
Vol 137 (04) ◽  
pp. 1245-1254 ◽  
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov ◽  
Susan Montgomery
Keyword(s):  
Lie Algebras ◽  
Positive Characteristic ◽  
Simple Lie Algebras ◽  
Group Gradings

scholarly journals Classification of group gradings on simple Lie algebras of types A, B, C and D

2010 ◽  
Vol 324 (11) ◽  
pp. 2971-2989 ◽  
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Group Gradings

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras
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