## Group theory – Week 07

For our purposes, a Lie algebra is defined as a linear vector space with elements with real or complex numbers. The Lie algebra has a bilinear operation that satisfies:

- closure: For
- antisymmetry:
- linearity of the bracket:
- associativity:

A vector in is going to be expanded in terms of the generators . The structure constants are defined by

We will be considering real forms, where the structure constants are always real numbers.

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