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- W2036032617 abstract "A characterization of Lie algebras of skew-symmetric elements of associative algebras with involution is obtained. It is proved that a Lie algebra L is isomorphic to a Lie algebra of skew-symmetric elements of an associative algebra with involution if and only if L admits an additional (Jordan) trilinear operation {x,y,z} that satisfies the identities $${x,y,z}={z,y,x},$$$$[[x,y],z]={x,y,z}-{y,x,z},$$$$[{x,y,z},t]={[x,t],y,z}+{x,[y,t],z}+{x,y,[z,t]},$$$${{x,y,z},t,v}={{x,t,v},y,z}-{x,{y,v,t},z}+{x,y,{z,t,v}},$$where [x,y] stands for the multiplication in L." @default.
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- W2036032617 date "2005-01-01" @default.
- W2036032617 modified "2023-09-28" @default.
- W2036032617 title "A Characterization of Lie Algebras of Skew-Symmetric Elements" @default.
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- W2036032617 doi "https://doi.org/10.1007/s10440-004-5598-0" @default.
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