Zero product determined classical Lie algebras
Zero product determined classical Lie algebras
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DOI：
10.1080/03081080903191672
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发表时间：
2010-04
影响因子：
1.1
通讯作者：
M. Grasic
中科院分区：
文献类型：
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作者：
M. Grasic
证明了关于转置对合或辛对合的反对称矩阵的李代数ℒ是零积决定的。这意味着如果满足下列条件：[x，y]=0表示从ℒ×ℒ到向量空间X的每个双线性映射{x，y}=T([x，y])对于某个线性映射T是{x，y}=T([x，y])。
We show that the Lie algebra ℒ of skew-symmetric matrices with respect to either transpose or symplectic involution is zero product determined. This means that every bilinear map {·,·} from ℒ × ℒ into a vector space X is of the form {x, y} = T ([x, y]) for some linear map T provided that the following condition is fulfilled: [x, y] = 0 implies {x, y} = 0.