6533b7cffe1ef96bd1259aca

RESEARCH PRODUCT

Lie Algebras Generated by Extremal Elements

Aaron CohenAnja SteinbachRosane UshirobiraDavid B. Wales

subject

17B05[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Non-associative algebraAdjoint representationGroup Theory (math.GR)01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Graded Lie algebraCombinatoricsMathematics - Algebraic Geometry0103 physical sciences[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]FOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]MathematicsDiscrete mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematics[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]20D06[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Rings and AlgebrasKilling formAffine Lie algebra[ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]Lie conformal algebra[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Adjoint representation of a Lie algebraRings and Algebras (math.RA)17B05; 20D06010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Group Theory

description

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

yearjournalcountryeditionlanguage
1999-03-12Journal of Algebra
10.1006/jabr.2000.8508http://dx.doi.org/10.1006/jabr.2000.8508