2 problems

Let $g=\bigoplus_{k=1}^n g_k$ be the direct sum of simple Lie algebras, let $\rho=\sum_{k=1}^n\rho_k$ be its Weyl vector, and set … The simple real roots span $\mathfrak{h}^*$, so…

Let $\mathfrak{g}=\mathfrak{h}\oplus\bigoplus_{\alpha\ne 0}\mathfrak{g}_\alpha$ be the Borcherds–Kac–Moody Lie algebra associated with a general Nakajima variety, with finite-dimen…