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skew-commutative algebra

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

  • xy=(1) pqyxx \wedge y = (-1)^{pq}\, y \wedge x whenever xx is in grade pp and yy is in grade qq.

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

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