
#1
Aug711, 04:59 PM

P: 67

hi friends !!
it is well known that a Lie algebra over K is a Kvector space g equipped of a Kbilinear, called Lie bracket. I ask how can we determines the Lie algebra of any vector space then? For example we try the Lie algebra of horizontal space. 



#2
Aug711, 05:19 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

You seem to have the idea that there is such a thing as "the" Lie Algebra of a vector space. That's not true. There exist an infinite number of Lie Algebras for a given vector space.



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