Hi I'm studying the paper "Twisted Graded Algebras and Equivalences of Graded Categories" by J.J Zhang. At one point the statement is made "Note that a $k$-linear graded automorphism of $A$ is not necessarily an automorphism of algebras".
Where $A$ is a graded algebra $A=\bigoplus_{g\in\mathbb{G}}A_{g}$
Any ideas to understand it better or find a counter example?
Also, if you've studied on this topic, I would appreciate if you've any reference.
Thanks so much.
2026-03-25 19:06:57.1774465617
A $k$-linear graded automorphism of $A$ is not necessarily an automorphism of algebra.
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