Eric Forgy graded differential algebra

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Definition

A graded differential algebra is a graded algebra

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

together with a derivation

d:\Omega^r\to\Omega^{r+1}

satisifying

d^2 = 0

and

d(\alpha\beta) = (d\alpha)\beta + (-1)^{|\alpha|} \alpha(d\beta),

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

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

category: maths

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