skew-commutative algebra

A **skew-commutative algebra** is a graded algebra $A$ (with the product often written as $\wedge$) such that

- $x \wedge y = (-1)^{pq}\, y \wedge x$ whenever $x$ is in grade $p$ and $y$ is in grade $q$.

Actually, there is a *twisted tensor product* on the category $Gr Mod$ of graded modules such that a skew-commutative algebra is really a commutative algebra (that is an abelian monoid object) in $Gr Mod$, but I forget how that goes.

Created on July 29, 2009 at 21:50:06. See the history of this page for a list of all contributions to it.