Associative/Lie radical (co)invariance under tracial (co)actions

Abstract

We prove a number of Jacobson/solvable/nilpotent-radical (co)invariance results for finite-dimensional associative or Lie (co)module-algebras over Hopf algebras $H$, provided the characteristic, if positive, is large relative to the dimension of the algebra and the (co)actions satisfy trace-preservation conditions automatic when $H$ is involutory. This generalizes a number of such radical-invariance criteria in the literature, due to A. Gordienko, V. Linchenko, Pagon-Repov{š}-Zaicev and others, providing a uniform enriched-categorical framework for those results.

6 pages + references