Assume we have a complex vector space $V$ and an involution $\omega:V\to V$, that is $\omega²=id$.
Does this give a $\mathbb{Z}_2$-grading of $V$ somehow?
2026-02-22 19:30:02.1771788602
$\mathbb{Z}_2$-grading of a vector space by an involution
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A $\Bbb Z/2 \Bbb Z$-grading is a spitting $V \cong V_0 \oplus V_1$. $V$ splits as the $1$-eigenspace and the $-1$-eigenspace with respect to $\omega$, so this give two natural gradings on $V$.