Completeness of the Sklyanin-algebra isomorphism classification

Prove the unresolved special-line and characteristic-two components needed to establish necessary and sufficient conditions for isomorphisms among three-generator Sklyanin algebras over arbitrary fields, including the assertion that no further isomorphisms occur beyond equality up to common nonzero scale or exchange of the first two parameters.

Background

The benchmark problem extends an existing classification of three-generator Sklyanin algebras to exceptional parameter families and fields of characteristic three or lacking a nontrivial cubic root of unity. A complete result must handle descent from an algebraic closure to the original field and prove both necessity and sufficiency of the proposed parameter relation.

The paper reports that one attempted solution leaves a special-line component hypothesis and a characteristic-two proof unresolved. It identifies the remaining no-further-isomorphisms assertion as the key gap separating evidence for the proposed classification from a proof covering every required field and parameter stratum.