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In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. In most of these theories, the ''even'' elements of the superalgebra correspond to bosons and ''odd'' elements to fermions (but this is not always true; for example, the BRST supersymmetry is the other way around). ==Definition== Formally, a Lie superalgebra is a (nonassociative) Z2-graded algebra, or ''superalgebra'', over a commutative ring (typically R or C) whose product , called the Lie superbracket or supercommutator, satisfies the two conditions (analogs of the usual Lie algebra axioms, with grading): Super skew-symmetry: : The super Jacobi identity: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lie superalgebra」の詳細全文を読む スポンサード リンク
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