2015/12/30 by Cagliero, Leandro, Szechtman, Fernando
#15A21 #17-08 #17B05 #FOS: Mathematics #Representation Theory (math.RT) #Secondary 20C40
paper · doi:10.48550/arxiv.1512.09096
We prove that if \mathfraks is a solvable Lie algebra of matrices over a field of characteristic 0, and A∈\mathfraks, then the semisimple and nilpotent summands of the Jordan-Chevalley decomposition of A belong to \mathfraks if and only if there exist S,N∈\mathfraks, S is semisimple, N is nilpotent (not necessarily [S,N]=0) such that A=S+N.