\ ¦lē \
Definition of Lie algebra
: a linear algebra which has the multiplicative operation denoted by [, ] and is bilinear such that [aA + bB,C] = a[A,C] + b[B,C] and [A,aB + bC] = a[A,B] + b[A,C] and satisfies the conditions that [A,A] = 0 and [[A,B],C] + [[B,C],A] + [[C,A],B] = 0 where A, B, C are any vectors in the vector space and a, b, c are scalars from the associated field
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