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Chapter 22: Lie Groups and Lie Algebras
https://doi.org/10.1142/9789813275386_0022Cited by:0 (Source: Crossref)
Abstract:
A Lie algebra is defined as follows: A vector space L over a field F, with an operation L × L → L denoted by (x, y) → [x, y] and called the commutator of x and y, is called a Lie algebra over F if the following axioms are satisfied:
(L1) The bracket operation is bilinear:
(L2) [x, x] = 0 for all x ∊ L
(L3) [x, [y, z]] + [y, [z, x]] + [z, [x, y]] = 0 (x, y, z ∊ L).
Axiom (L3) is called the Jacobi identity…
