Graded group actions and generalized H-actions compatible with gradings

We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseu-doautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super-or a pseudoinvolu-tion. We study groups of graded pseudoautomorphisms, show that the Jacobson radical of a group graded finite dimensional associative algebra A over a field of characteristic 0 is stable under graded pseudoautomorphisms, prove the invariant ver-sion of the Wedderburn-Artin Theorem and the analog of Amitsur's conjecture for the codimension growth of graded polynomial G-identities in such algebras A with a graded ac-tion of a group G. (c) 2023 Elsevier Inc. All rights reserved.