Poincaré duality in modular coinvariant rings

Abstract

We classify the modular representations of a cyclic group of prime order whose corresponding rings of coinvariants are Poincaré duality algebras. It turns out that these algebras are actually complete intersections. For other representations we demonstrate that the dimension of the top degree of the coinvariants grows at least linearly with respect to the number of summands of dimension at least four in the representation. © 2016 American Mathematical Society.