Generalized cross product in R 6 and R m , m= n(n - 1)/2

Authors : Bülent KARAKAŞ

Pages : 0-0

Doi:10.1501/Commua1_0000000531

View : 45 | Download : 14

Publication Date : 1990-01-01

Article Type : Research Paper

Abstract :In this study in the space R®, the cross-product was defined as analogous vector-product in R3. We showed that this product makes R3 a Lie algebra. Therefore, it was showed that the Lie algebras insert ignore into journalissuearticles values(R®,0); and insert ignore into journalissuearticles values(A4, [,]); are isomorphic. As a generalization, in the space of dimension m — n insert ignore into journalissuearticles values(n -l);/2, cross-product can be given as Rm x Rm -> Rm , xoy = J” 1 [Jinsert ignore into journalissuearticles values(X);, Jinsert ignore into journalissuearticles values(Y);] where J — Rm -> An is Lie algebra isomorphism. At the end, we showed that the cross - product we defined is vector product well known for n = 3.
Keywords : space, analogous, algebras

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