Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order
type: Item
instance of: scholarly article
title: Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order
zbMATH Open document ID: 0809.16052
published in: Journal of Algebra
publication date: 1995-03-29T00:00:00Z
review text: In this paper the classification of all irreducible representations of the 4-dimensional Sklyanin algebra at points of infinite order is achieved. Let \(A\) denote a Sklyanin algebra constructed from an elliptic curve \(E\), a line bundle of degree 4 and a point (of infinite order) \(\tau\). In [\textit{E. K. Sklyanin}, Funkts. Anal. Prilozh. 17, 34-48 (1983; Zbl 0536.58007)], a family of finite dimensional modules \(V(k)\), \(k\) a non-negative integer, was constructed. It is shown in the present paper that these are irreducible, and that any irreducible representation can be obtained from some \(V(k)\) by twisting by an automorphism. The classification uses previous results from \textit{T. Levasseur} and \textit{S. P. Smith} [Bull. Soc. Math. Fr. 121, 35-90 (1993)], \textit{S. P. Smith} and \textit{J. T. Stafford} [Compos. Math. 83, 259-289 (1992; Zbl 0758.16001)]. See also the preceding review Zbl 0809.16051.
reviewed by: Nicolás Andruskiewitsch
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 436481
zbMATH Keywords: irreducible representations
zbMATH Keywords: 4-dimensional Sklyanin algebra
zbMATH Keywords: points of infinite order
zbMATH Keywords: elliptic curve
zbMATH Keywords: line bundle
zbMATH Keywords: finite dimensional modules
author: S. Paul Smith
author: Joanna M. Staniszkis
MaRDI profile type: Publication
full work available at URL: jabr.1993.1178
OpenAlex ID: W2166688297
DOI: 10.1006/JABR.1993.1178
description: scientific article; zbMATH DE number 436481