No isomorphism between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras

TL;DR

This paper clarifies that there is no isomorphism between the affine  algebra and the N=2 superconformal algebras, resolving longstanding confusion in the literature.

Contribution

It provides a definitive proof that no isomorphism exists between the affine  algebra and N=2 superconformal algebras, correcting prior misconceptions.

Findings

Confirmed the absence of isomorphism between the algebras.

Clarified misconceptions in existing literature.

Established a clear distinction between the algebraic structures.

Abstract

Since 1999 it became obvious that the would be `isomorphism' between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in the literature and, as a result, some confusion still remains. In this article we finally settle down, clearly and unambiguously, the true facts: there is no isomorphism between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras.