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…
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
- linearity of the bracket:
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.