2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119172Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such deformations and construct numerous examples. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures. We also describe an important class of M-structures related to the affine Dynkin diagrams of A, D, E-type. These M-structures and their representations are described in terms of quiver representations.26 pages, latexQuantum AlgebraRepresentation Theory17B80, 17B63, 32L81, 14H70text