Subject: Re: extension of Steenrod algebra Date: Mon, 2 Jul 2001 09:38:09 -0400 (EDT) From: "Michael J. Hopkins" Danny Arnon looked at this in his thesis from about 10 years ago. His investigations were in connection with a question of Frank Peterson. The paper appeared in the Israeli Journal of mathematics @article {MR1776082, AUTHOR = {Arnon, Dan}, TITLE = {Generalized {D}ickson invariants}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {118}, YEAR = {2000}, PAGES = {183--205}, } Mike --- Michael Hopkins MIT --- > > Subject: question for topology list > Date: 27 Jun 2001 17:50:04 -0700 > From: palmieri@math.washington.edu (John H. Palmieri) > > Has anyone come across the following thing? I would call it the > Steenrod algebra with the Frobenius map inverted. Let p=2. Consider > > F_2 [xi_1, xi_2, xi_3, ... > plus all square roots of the xi_i's, all 4th roots, all 8th > roots, etc.] > > Put the usual coproduct on this: > > xi_n^{2^j} -> Sum_i xi_{n-i}^2^{i+j} tensor xi_i^2^j, > > except this is valid for all integers j, not just non-negative ones. > Then I think this becomes a Hopf algebra, using Milnor's formula for > the antipode. It's Z[1/2]-graded, zero in negative degrees. You can > of course do the same thing when p is odd, using only the reduced > powers part of the Steenrod algebra. > > So, what is its Ext algebra? It should be Ext over the Steenrod > algebra with Sq^0 inverted, but what's that? > > -- > J. H. Palmieri > Dept of Mathematics, Box 354350 mailto:palmieri@math.washington.edu > University of Washington > http://www.math.washington.edu/~palmieri/ > Seattle, WA 98195-4350 > >