Let A be a symmetrizable generalized Cartan matrix, g(A) thecorresponding Kac-Moody algebra, then a subalgebra h of g(A) is a split Cartan subalgebra if and only if there is a regular locally finite element x such that h=g 0(adx).

 
  • 設A為一可對稱(chēng)化廣義Cartan矩陣 ;g(A)為對應的Kac_Moody代數 ;則 g(A)的子代數h為可裂Cartan子代數的充分必要條件為存在正則局部有限元x ;使得h =g0 (adx) .
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