Notes for AKT-091001-2/0:20:46

Examples:

1.[math]\displaystyle{ \mathcal{G}=\mathbb{Q}^n }[/math] with [math]\displaystyle{ [ \cdot , \cdot ] = \overline{0} }[/math]

2. [math]\displaystyle{ \mathcal{G} = gl_n }[/math] with [math]\displaystyle{ [A, B]=AB-BA }[/math]

3. [math]\displaystyle{ \mathcal{G} = }[/math] set of all anti-symmetric matrices in [math]\displaystyle{ gl_n }[/math] with the bracket as defined in [math]\displaystyle{ gl_n }[/math]

4. [math]\displaystyle{ FL_2(x,y)= }[/math] set of all trees with leaves labeled with symbols [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] mod AS and STU with [math]\displaystyle{ [\cdot, \cdot] }[/math] being the operation that connects the roots of the trees

5. Given two Lie-algrbras, the direct sum of them is a Lie-algrbra.