# Exterior and tensor product of algebras

Hi,

I've been trying to construct something like $\Lambda^2 A \otimes A$ where $A$ is a free associative $\mathbb{Q}$-algebra on some generators, say, $x$ and $y$, without success. I think I understand the basics of the FreeAlgebra object in Sage, but I could not find more specific information about this kind of construction in the documentation or here in this forum. Ultimately, I would like to form and calculate with expressions like $x y \wedge xx \otimes xy$ where $x,y\in \mathbb{Q}\langle x,y\rangle$, the free associative unital algebra, and such that, for instance, $xy \wedge xx \otimes xy = - xx \wedge xy \otimes xy$. Does anyone know whether this is or is not possible to achieve in Sage at the moment? Any help will be greatly appreciated.

Cheers,

Waldeck

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