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0XXXXX 1-2 The last 2.1 is valid 2n-dimensional vector space 57 for Eg algebra of type algebras with fundamental apply exp(ad assume that Lemma automorphism exp(ad basis element bilinear form Cartan subalgebra classical Lie algebras complex numbers conjugate Cornell University corresponds a basis denoted direct sum division ring Dynkin diagram element in Eg Ellensburg Exceptional characteristics exists an automorphism exp(ad ye finite characteristic fundamental system Gordon Elliott Brown last column exists Lemma 2.X Lemma II1 Lie product linear dependence relation linearly independent mapping matrix of trace mihi+ non-singular non-zero roots positive roots preceding Lemma 3.1 Proof of Lemma prove root f simple Lie algebras simple root skew-symmetric linear transformations subspace Suppose system of roots teristic p>2 Theorem 2.1 thesis trace zero type Bn Witt algebra X 0 X XX22XXX XX2CC2X XXX2XX yields an element zero Is expressible