Speaker: Andrew Baker (University of Glasgow, Scotland)
Abstract: For a prime number $p$, the mod $p$ Steenrod algebra is the Hopf algebra of stable operations in mod $p$ cohomology. As an algebra this is an infinite dimensional non-commutative graded local ring in which every positive degree element is nilpotent; the dual Hopf algebra is an infinitely generated free commutative algebra. What makes this ring tractable is the fact that it is a union of finite dimensional subHopf algebras each of which is a Poincar\’e duality algebra (this is the graded analogue of a Frobenius algebra). This leads to many useful properties of modules over it, reminiscent of those of a Poincar\’e duality and Frobenius algebras; indeed Moore \& Peterson called such Hopf algebras \emph{nearly Frobenius}. I will explain this and some calculational consequences, then talk about a non-graded version of this theory which I developed during the Covid lockdown period.
Time: 5 pm, Wednesday, 26th February
Venue: Room 1610 (online speaker)
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