Eric Forgy graded differential algebra

Definition

A graded differential algebra is a graded algebra

Ω= r=0 nΩ r\Omega = \bigoplus_{r=0}^n \Omega^r

together with a derivation

d:Ω rΩ r+1d:\Omega^r\to\Omega^{r+1}

satisifying

d 2=0d^2 = 0

and

d(αβ)=(dα)β+(1) |α|α(dβ),d(\alpha\beta) = (d\alpha)\beta + (-1)^{|\alpha|} \alpha(d\beta),

where |α||\alpha| is the degree of α\alpha, i.e.

|α|=rαΩ r.|\alpha| = r\Leftrightarrow \alpha\in\Omega^r.

category: maths

Revised on January 5, 2009 at 19:34:48 by Eric Forgy