Subject: new Hopf listings From: Mark Hovey Date: 09 Dec 1999 20:32:42 -0500 I thought the last message was my last this century, but suddenly there are three more papers. Mark Hovey New papers uploaded to hopf between 12/8/99 and 12/9/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Benson-KrauseH/pureinj Title: Pure injectives and the spectrum of the cohomology ring of a finite group Authors: David Benson and Henning Krause E-mail: djb@byrd.math.uga.edu henning@mathematik.uni-bielefeld.de Abstract: For a finite group and a field of prime characteristic, we study certain pure injective representations in terms of the spectrum of the group cohomology ring. This includes a complete classification of all representations which arise as a direct summand of a (possibly infinite) product of syzygies of the trivial representation. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Pengelley-Peterson-Williams/gl obstr (That's "Global Structure", not "g lobster" :) ) A global structure theorem for the mod two Dickson algebras, and unstable cyclic modules over the Steenrod and Kudo-Araki-May algebras David J. Pengelley davidp@nmsu.edu Franklin P. Peterson fpp@math.mit.edu Frank Williams frank@nmsu.edu The Dickson algebra W_{n+1} of invariants in a polynomial algebra over F_2 is an unstable algebra over the mod 2 Steenrod algebra A, or equivalently, over the Kudo-Araki-May algebra K of ``lower'' operations. We prove that W_{n+1} is a free unstable algebra on a certain cyclic module, modulo just one additional relation. To achieve this, we analyze the interplay of actions over A and K to characterize unstable cyclic modules with trivial action by the subalgebra A_{n-2} on a fundamental class in degree (2^n)-a, where a is a nonnegative integer. This involves a new family of left ideals I_a in K, which play the role filled by the ideals generated by A_{n-2} in the Steenrod algebra. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Pengelley-Williams/limalg Limits of algebras with shifting and a relationship between the mod two Steenrod and Dyer-Lashof algebras David J. Pengelley davidp@nmsu.edu Frank Williams frank@nmsu.edu We provide a construction, refined from an inverse limit, that produces the mod 2 Steenrod and Dyer-Lashof algebras from each other. In fact, the construction relates various subalgebras and quotients of the universal Steenrod algebra of operations for H-infinity ring spectra. We also describe how the construction transforms the axiomatic properties of homogeneous pre-Koszul algebras and Poincare-Birkhoff-Witt algebras. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://www.math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/algtop.html which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. The largest archive of math preprints is at http://xxx.lanl.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/pub/new-html/submissions.html In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.