Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order (Q687660)

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.