Zero product determined Jordan algebras,I |
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Authors: | Mateja Grašič |
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Institution: | 1. IMFM , Jadranska 19, Ljubljana, Slovenia mateja.grasic@uni-mb.si |
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Abstract: | We show that the Jordan algebra 𝒮 of symmetric matrices with respect to either transpose or symplectic involution is zero product determined. This means that if a bilinear map {.,?.} from 𝒮?×?𝒮 into a vector space X satisfies {x, y}?=?0 whenever x?○?y?=?0, then there exists a linear map T : 𝒮?→?X such that {x,?y}?=?T(x?○?y) for all x, y?∈?𝒮 (here, x?○?y?=?xy?+?yx). |
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Keywords: | zero product determined Jordan algebra symmetric matrix transpose involution symplectic involution bilinear map linear map |
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