In the context of linar algebraic groups, I read in my notes from the lecture that's already some while ago that $GL_n(k)$ is an algebraic variety because $GL_n=D(\det)$, $ \det \in k [ (X_{ij})_{i,j} ]$. Now, $k$ is an algebraically closed field, $\det$ is the determinant and $k [ (X_{ij})_{i,j} ]$ are the polynomials in unkwnowns $X_{ij}$. But I cannot find what $D$ meant, maybe it's also a typo or uncommon notation -.-
How can I interpret $GL_n (k)$ as a variety? (Or what does this $D$ stand for?)