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NOVA JOURNAL OF ALGEBRA
DECOMPOSITIONS OF BRUHAT TYPE FOR KACMOODY GROUPS
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2-group a a a a a abelian group acts quadratically Algebra and Geometry algebra of order alternative ring amalgams assume Bernstein algebra Bruhat Bruhat decomposition central characteristic subgroup commutative completes the proof contradiction coplanar Corollary d(a,a+b d(b,b+a decomposition define denote Department of Mathematics direct sum disjoint duads elementary abelian elements exists finite fixes follows full orthogonal multiplication group rings Hence hexad containing ideal idempotents implies invariant involution isomorphic Journal of Algebra Lemma Let G Let h linear loop rings Math Moreover Moufang nilpotent non-trivial nonzero normal normal subgroup notation Nova Journal Nova Science Publishers obtain orthonormal paper parabolic geometry power-associative proof of Theorem prove Q Q I quaternion RA loop result right alternative Rm+1 Rm+2 semiprime subgroup of G subject classification subloop superalgebra Suppose torsion units transvection triduad unique vector whence Z Q Q