SHEARED ALGEBRA MAPS AND OPERATION
BIALGEBRAS FOR MOD 2 HOMOLOGY AND
COHOMOLOGY
DAVID J. PENGELLEY AND FRANK WILLIAMS
Abstract. The mod 2 Steenrod algebra A and Dyer-Lashof al-
gebra R have both striking similarities and differences, arising
from their common origins in "lower-indexed" algebraic operations.
These algebraic operations and their relations generate a bigraded
bialgebra K, whose module actions are equivalent to, but quite dif-
ferent from, those of A and R. The exact relationships emerge as
"sheared algebra bijections", which also illuminate the role of the
cohomology of K. As a bialgebra, K* has a particularly attractive
and potentially useful structure, providing a bridge between those
of A* and R*, and suggesting possible applications to the Miller
spectral sequence and the A structure of Dickson algebras.
New Mexico State University, Las Cruces, NM 88003
E-mail address: davidp@nmsu.edu
E-mail address: frank@nmsu.edu