Co-stability of radicals and its applications to PI-theory
Abstract
We prove that if A is a finite dimensional associative H-comodule algebra over a field F for some involutory Hopf algebra H not necessarily finite dimensional, where either char F = 0 or char F > dim A, then the Jacobson radical J(A) is an H-subcomodule of A. In particular, if A is a finite dimensional associative algebra over such a field F, graded by any group, then the Jacobson radical J(A) is a graded ideal of A. Analogous results hold for nilpotent and solvable radicals of finite dimensional Lie algebras over a field of characteristic 0. We use the results obtained to prove the analog of Amitsur's conjecture for graded polynomial identities of finite dimensional associative algebras over a field of characteristic 0, graded by any group.
Keywords
Cite
@article{arxiv.1301.2446,
title = {Co-stability of radicals and its applications to PI-theory},
author = {Alexey Sergeevich Gordienko},
journal= {arXiv preprint arXiv:1301.2446},
year = {2017}
}
Comments
9 pages; definitions and introduction overlap with arXiv:1203.5384 and arXiv:1205.0778