Hall polynomials for Nakayama algebras

Abstract

Let A be a representation finite algebra over finite field k. In this note we first show that the existence of Hall polynomials for A equivalent to the existence of the Hall polynomial φ NL M for each M, L ∈ modA and N ∈ indA. Then we show that for a basic connected Nakayama algebra A, ℋ (A)= ℒ(A) and Hall polynomials exist for this algebra. We also provide another proof of the existence of Hall polynomials for the representation directed split algebras. © 2010 Springer Science+Business Media B.V.