Central elements and evaluation map for the quantum queer superalgebras

TL;DR

This paper studies the structure of quantum queer superalgebras, deriving crossing symmetry relations for their R-matrices, constructing central elements, and establishing an epimorphism linking affine and finite versions.

Contribution

It introduces new crossing symmetry relations, constructs central elements, and defines an epimorphism between affine and finite quantum queer superalgebras.

Findings

Derived crossing symmetry relations for R-matrices.

Constructed central elements in superalgebras.

Established an epimorphism from affine to finite superalgebra.

Abstract

We consider the $R$-matrix presentations of the quantum queer superalgebra $U_q(q_n)$ and its affine counterpart $U_q(\widehat q_n)$. We derive crossing symmetry relations for the $R$-matrices and use them to construct central elements in both superalgebras. We also produce an epimorphism $ev:U_q(\widehat q_n)\to U_q(q_n)$ identical on the subalgebra isomorphic to $U_q(q_n)$.