2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185750n^{th} root of a Lie algebra and its dual (that is fractional supergroup) based on the permutation group $S_n$ invariant forms are formulated in the Hopf algebra formalism. Detailed discussion of $S_3$-graided $sl(2)$ algebras is done.13 pages, detailed discussion of $S_3$-graided $sl(2)$ is addedRepresentation TheoryHigh Energy Physics - TheoryMathematical PhysicsGroup TheoryQuantum Algebratext