Two responses to yesterdya's question about sign conventions....DMD
____________________________________

Subject: Re: two questions
Date: Mon, 10 Jun 2002 12:04:19 -0400 (Eastern Daylight Time)
From: Steve Halperin <shalper@deans.umd.edu>

With respect to Jim's question, I am used to calling it the
Koszul convention. Koszul himself may know the reference,
but so should Lemaire.

                 steve halperin
On Mon, 10 Jun 2002 11:29:46 -0400 Don Davis
<dmd1@lehigh.edu> wrote:


> Subject: query
> Date: Sat, 08 Jun 2002 11:36:21 -0400
> From: jim stasheff <stasheff@email.unc.edu>
>
>  With regard to the convention that the interchange
> rule for any two graded thing:
>
> I wrote an author:
> > The sign convention you use is more usually called Koszul's or Mac
> Lane's.
>
> He responded:
> ``Finding the proper reference for this convention
> would cause me a lot of trouble.
> Do you know the source of the sign rule?''
>
> For graded algebras, graded commutativity used this sign long long ago
> e.g. at least in the wedge product of diff forms
> but who first used it for e.g. moving a function past an element?
>
> ( f \otimes g) (x \otimes y) = (-1)^{ deg g deg s} f(x) \otimes g(y)
>
> ??
>
> and who first ennuciated it as a general principle?
>
> I remember at IAS aftr the summer of foliation in Mexico there was
> ` a fundamental contradiciton' in math because people had NOT applied
> the rule consistently
>
> jim
> ________________________________________________


----------------------
Steve Halperin, Dean
shalper@deans.umd.edu
____________________________________________

Subject: Re: two questions
Date: Mon, 10 Jun 2002 17:23:02 -0700
From: Hans Samelson <samelson@math.stanford.edu>

I remember from "way back" when Eilenberg and Maclane started their
collaboration that they sent around a flyer to all mathematicians
explaining (as I remember) that the interchange rule had become so all
pervasive that they proposed the Weierstrass p
as the universal symbol for the parity of an object x (in the form p(x) ),
instead of the many  ( - 1)^degree, ( - 1)^|...| and other ad hoc
expressions. (It didn't pass.)
 ----  Another candidate for who stated the general rule: Mike
Boardman.      Hans Samelson