Two more responses re sign conventions.......DMD
_____________________________________________

Subject: Re: 2 responses
Date: 11 Jun 2002 14:15:58 +0100
From: N.P.Strickland@sheffield.ac.uk

This reference is the only systematic discussion of signs that I know
of:

@article {MR35:236,
    AUTHOR = {Boardman, J. M.},
     TITLE = {The principle of signs},
   JOURNAL = {Enseignement Math. (2)},
    VOLUME = {12},
      YEAR = {1966},
     PAGES = {191--194},
   MRCLASS = {18.20 (08.00)},
  MRNUMBER = {35 \#236},
MRREVIEWER = {E. Hemmingsen},
}

Neil
________________________________________

Subject: RE: two questions
Date: Tue, 11 Jun 2002 09:20:33 -0400
From: Ron Umble <Ron.Umble@millersville.edu>

MacLane states what he calls the "standard sign commutation rule"
in his text "Homology," p. 164.

Ron Umble

-----Original Message-----

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