Algebras and Representation Theory

, Volume 15, Issue 3, pp 483–490 | Cite as

Hall Polynomials for Nakayama Algebras

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Abstract

Let \(\mathcal{A}\) be a representation finite algebra over finite field k. In this note we first show that the existence of Hall polynomials for \(\mathcal{A}\) equivalent to the existence of the Hall polynomial \(\varphi^{M}_{N L}\) for each \(M, L \in mod\mathcal{A}\) and \(N\in ind\mathcal{A}\). Then we show that for a basic connected Nakayama algebra \(\mathcal{A}\), \(\mathcal{H}(\mathcal{A})=\mathcal{L}(\mathcal{A})\) and Hall polynomials exist for this algebra. We also provide another proof of the existence of Hall polynomials for the representation directed split algebras.

Keywords

Hall polynomials Nakayama algebras Representation finite algebras 

Mathematics Subject Classifications (2010)

16G20 17B37 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

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