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

Yıl 1990, Cilt: 39 , - , 01.01.1990

Bülent Karakaş

https://doi.org/10.1501/Commua1_0000000531

Öz

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 (R®,0) and (A4, [,]) are isomorphic. As a generalization, in the space of dimension m — n (n -l)/2, cross-product can be given as
Rm x Rm -> Rm , xoy = J” 1 [J(X), J(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.

Anahtar Kelimeler

space, analogous, algebras

Kaynakça

• Communications, Series A1:Mathematics and Statistics