The equitable q-deformation of sl2

In this paper, we investigate the algebra U-q(Delta)(sl(2)), which is known as the equitable q-deformation of sl(2). This algebra was introduced in 2005 by Ito et al. Assume that q is a primitive mth root of unity with m >= 3. We prove that U-q(Delta)(sl(2)) becomes a Polynomial Identity (PI) algebra. It was previously known for such algebras, the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of U-q(Delta)(sl(2)), and we classify up to isomorphism the simple U-q(Delta)(sl(2))-modules. We also find the center of U-q(Delta)(sl(2)).