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Orthogonal decompositions of classical Lie algebras over finite commutative rings
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Orthogonal decompositions of classical Lie algebras over finite commutative rings
classification
math.RA
keywords
orthogonalalgebracommutativedecompositionsfinitespecialadditionallyalgebras
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Let $R$ be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over $R$. Additionally, we study orthogonal decompositions of the symplectic Lie algebra and the special orthogonal Lie algebra over $R$.
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