# classification – \$mathfrak{su}(N)\$ lie algebra

In the context of semisimple lie algebra, over $$mathbb{k}$$ algebraic closed and of characteristic zero, one can classifie all of then in $$mathfrak{sl}_n(mathbb{k})$$, $$mathfrak{so}_{2n}(mathbb{k})$$, $$mathfrak{so}_{2n+1}(mathbb{k})$$ and $$mathfrak{sp}_{2n}(mathbb{k})$$. My question is: which algebra corresponds to the $$mathfrak{su}_n(mathbb{C})$$?