Is $\mathfrak{gl}_2$ a Kac-Moody Lie Algebra?

Question

Is $\mathfrak{gl}_2$ a Kac-Moody Lie Algebra?

For the definition of Kac-Moody algebra, I was using "Introduction to Quantum Groups and Crystal Bases" by Hong and Kang.

Edit: On page 150 in the book mentioned above, they provide the Cartan matrix and Dynkin diagram for $\mathfrak{gl}_n$. So it seems that $\mathfrak{gl}_2$ is a Kac-Moody Lie algebra. I will try to go through and confirm this.