name of a special map sought

Question

I'm playing with some mathematical stuff. More precisely, I'm considering maps

$ T \colon X \to X$

for an arbitrary set $X$, where $T$ has the property:

$T^2 = T \circ T = -T$.

In other words : $T^2$ maps to its negative value.

My question : Is there a name (designation) for maps mentioned above?

Thanks in advance.

edit: Maybe there is no official name for that. I tried to google it, but I found nothing helpful. For me, this is an interesting subject and I just wanted to know if there is a designation or if there are already some scientific results for such maps.

Answer 1

If it weren't for the minus sign, $T$ would be idempotent. With the minus sign, a simple name might therefore be skew- or anti-idempotent. A search of these phrases through Google Scholar does give some hits to that effect, with more for the latter than the former.