2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153842Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the dynamical $r$-matrices.14 pages, LatexExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryQuantum Algebratext