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

Alexandru Chirvasitu

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arXiv · 2608.04851

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

Alexandru Chirvasitu

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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{\v{s}}-Zaicev and others, providing a uniform enriched-categorical framework for those results.

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BibTeX RIS

Alexandru Chirvasitu. 2026-08-05. Associative/Lie radical (co)invariance under tracial (co)actions. https://arxiv.org/abs/2608.04851

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