Taw Pin Lim, "Rings with involution whose symmetric elements are central", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 762359, 7 pages, 1980. https://doi.org/10.1155/S0161171280000178
Rings with involution whose symmetric elements are central
In a ring with involution whose symmetric elements are central, the skew-symmetric elements form a Lie algebra over the commutative ring . The classification of such rings which are -torsion free is equivalent to the classification of Lie algebras over equipped with a bilinear form that is symmetric, invariant and satisfies . If is a field of char , and then is a semisimple Lie algebra if and only if is nondegenerate. Moreover, the derived algebra is either the pure quaternions over or a direct sum of mutually orthogonal abelian Lie ideals of .
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