An algorithm for the periodicity of deformed preprojective algebras of Dynkin types E6, E7 and E8

Jerzy Białkowski

Applied Mathematics and Computation, 2021, vol. 409, issue C

Abstract: We construct a numeric algorithm for completing the proof of a conjecture asserting that all deformed preprojective algebras of generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing that non-trivial deformed preprojective algebras of Dynkin types E7 and E8 exist only in characteristic 2. As a consequence, we show that deformed preprojective algebras of Dynkin types E6,E7 and E8 are periodic and we obtain an algorithm for a classification of such algebras, up to algebra isomorphism. We do it by a reduction of the conjecture to a solution of a system of equations associated with the problem of the existence of a suitable algebra isomorphism φf:Pf(En)→P(En) described in Theorem 2.1. One also shows that our algorithmic approach to the conjecture is also applicable to the classification of the mesh algebras of generalized Dynkin type.

Keywords: Preprojective algebra; Deformed preprojective algebra; Self-injective algebra; Periodic algebra; System of equations (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321003787

DOI: 10.1016/j.amc.2021.126289

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