On some Hall polynomials over a quiver of type ˜D4

Author:

Szántó Csaba1,Szöllősi István1

Affiliation:

1. Babeş-Bolyai University , Cluj-Napoca, Faculty of Mathematics and Computer Science , Str. Mihail Kogalniceanu nr. 1 R0-400084 Cluj-Napoca , Romania

Abstract

Abstract Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials F xy z associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference7 articles.

1. [1] I. Assem, D. Simson, A. Skowronski, Elements of Representation Theory of Associative Algebras, Volume 1: Techniques of Representation Theory, LMS Student Texts (No. 65), Cambridge Univ. Press 2006.

2. [2] M. Auslander, I. Reiten, S. Smalo, Representation Theory of Artin Algebras, Cambridge Stud. in Adv. Math. 36, Cambridge Univ. Press 1995.

3. [3] V. Dlab, C. M. Ringel, Indecomposable representations of graphs and algebras, AMS Memoirs 173, 1976.

4. [4] A. Hubery, Hall polynomials for affine quivers, Represent. Theory, 14 (2010), 355–378.

5. [5] C. M. Ringel, Hall algebras, in: Topics in algebra, Banach Center Publ., 26 (1990), 433–447.

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