Can you have axial vectors in a 2D space?
In a sense. The "axial vector" would be perpendicular to the plane.
I think such an object would be called a "twisted vector" or "odd vector".
from Bill Burke's pages http://www.ucolick.org/~burke/home.html
(You may need a postscript viewer like http://www.cs.wisc.edu/~ghost/gsview/ )
See also http://www.icm.edu.pl/edukacja/mat/axial.php
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