2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202861We present a uniform construction of level 1 perfect crystals $\mathcal B$ for all affine Lie algebras. We also introduce the notion of a crystal algebra and give an explicit description of its multiplication. This allows us to determine the energy function on $\mathcal B \otimes \mathcal B$ completely and thereby give a path realization of the basic representations at $q=0$ in the homogeneous picture.Representation TheoryQuantum Algebra17B37, 17B67, 81R50text