# nLab skew-commutative algebra

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

• $x\wedge y=\left(-1{\right)}^{\mathrm{pq}}\phantom{\rule{thinmathspace}{0ex}}y\wedge x$ whenever $x$ is in grade $p$ and $y$ is in grade $q$.

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

Created on July 29, 2009 21:50:06 by Toby Bartels (71.104.230.172)