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

Examples:

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

2. ${\mathcal {G}}=gl_{n}$ with $[A,B]=AB-BA$

3. ${\mathcal {G}}=$ set of all anti-symmetric matrices in $gl_{n}$ with the bracket as defined in $gl_{n}$

4. $FL_{2}(x,y)=$ set of all trees with leaves labeled with symbols $x$ and $y$ mod AS and STU with $[\cdot ,\cdot ]$ being the operation that connects the roots of the trees

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