## Catch up?

Yet another I-am-sorry-I-have-not-blogged-in-a-while”post. Will try to catch up on my past course material. Next semester seems pretty busy, at least in terms of coursework. It is now or never…

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## 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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