Yongcun Gao
Abstract
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).Further, a description of all regular locally finite elements is given.
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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).Further, a description of all regular locally finite elements is given.
Key concepts: Cartan subalgebra, Cartan matrix, Subalgebra, Mathematics, Kac–Moody algebra, Pure mathematics, Cartan decomposition, Algebra over a field