I recently came across the notation $\Lambda^2(\mathbb{R}^3)$. I believe this is a notation for the vector space of what some authors, such as William L. Burke, call twisted one-forms. That is, they behave like vectors under an orientation-preserving change of coordinates, but their direction has an external "screw-sense" rather than an internal orientation. I believe Burke's description is in the spirit of an older one by Schouten, but Burke's notation and coordinate-free approach are totally different.
Since I don't think Schouten or Burke's notation and terminology are widely understood by mathematicians, I would like to understand the system of notation to which the $\Lambda^2(\mathbb{R}^3)$ belongs. Can anyone tell me if I'm understanding it correctly, tell me what words correspond to the notation, and relate it to a broader system of notation, possibly referring to some published source? Unfortunately I came across this only in one of those peep-hole views of a book in google, and I failed to write down the name of the book. It's possible that I'm mistaken in my memory or understanding of the notation.
$\wedge^2(\Bbb R^3)$ is the second exterior power of $\Bbb R^3$. Hopefully that page proves useful.