Lie algebras generated by extremal elements
Cohen, Arjeh M. ; Steinbach, Anja ; Ushirobira, Rosane ; Wales, David B.
HAL, hal-00438549 / Harvested from HAL
Text on HAL
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.
Publié le : 1999-03-12
Classification:  [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] 
@article{hal-00438549,
     author = {Cohen, Arjeh M. and Steinbach, Anja and Ushirobira, Rosane and Wales, David B.},
     title = {Lie algebras generated by extremal elements},
     journal = {HAL},
     volume = {1999},
     number = {0},
     year = {1999},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00438549}
}

Cohen, Arjeh M.; Steinbach, Anja; Ushirobira, Rosane; Wales, David B. Lie algebras generated by extremal elements. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00438549/