3-Preprojective algebras of type D

Jordan Haden

doi:10.1007/s10468-024-10297-3

3-Preprojective algebras of type D

Jordan Haden

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Abstract

We present a family of selfinjective algebras of type D, which arise from the 3-preprojective algebras of type A by taking a ℤ₃-quotient. We show that a subset of these are themselves 3-preprojective algebras, and that the associated 2-representation-finite algebras are fractional Calabi-Yau. In addition, we show our work is connected to modular invariants for SU(3).

Original language	English
Pages (from-to)	2295–2320
Number of pages	26
Journal	Algebras and Representation Theory
Volume	27
Early online date	16 Nov 2024
DOIs	https://doi.org/10.1007/s10468-024-10297-3
Publication status	Published - Dec 2024

Keywords

16D50
16E35
16S35
2-Representation-finite
3-Preprojective
Fractional Calabi-Yau
Jacobian algebras
SU(3) modular invariants

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10.1007/s10468-024-10297-3Licence: CC BY

Haden_2024_ARTFinal published version, 1.16 MBLicence: CC BY

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keywords = "16D50, 16E35, 16S35, 2-Representation-finite, 3-Preprojective, Fractional Calabi-Yau, Jacobian algebras, SU(3) modular invariants",

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note = "Data Availability Statement: No datasets were generated or analysed during the current study. Funding information: This paper was written while the author was in reciept of a PhD studentship from the University of East Anglia.",

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N1 - Data Availability Statement: No datasets were generated or analysed during the current study. Funding information: This paper was written while the author was in reciept of a PhD studentship from the University of East Anglia.

PY - 2024/12

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N2 - We present a family of selfinjective algebras of type D, which arise from the 3-preprojective algebras of type A by taking a ℤ3-quotient. We show that a subset of these are themselves 3-preprojective algebras, and that the associated 2-representation-finite algebras are fractional Calabi-Yau. In addition, we show our work is connected to modular invariants for SU(3).

AB - We present a family of selfinjective algebras of type D, which arise from the 3-preprojective algebras of type A by taking a ℤ3-quotient. We show that a subset of these are themselves 3-preprojective algebras, and that the associated 2-representation-finite algebras are fractional Calabi-Yau. In addition, we show our work is connected to modular invariants for SU(3).

KW - 16D50

KW - 16E35

KW - 16S35

KW - 2-Representation-finite

KW - 3-Preprojective

KW - Fractional Calabi-Yau

KW - Jacobian algebras

KW - SU(3) modular invariants

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DO - 10.1007/s10468-024-10297-3

M3 - Article

SN - 1386-923X

VL - 27

SP - 2295

EP - 2320

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

ER -

3-Preprojective algebras of type D

Abstract

Keywords

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