Dynamical reflection equation

TL;DR

This paper develops a dynamical reflection equation algebra through a twist of the standard algebra, introduces a dynamical reflection equation, and constructs central elements using a new dynamical trace, advancing the algebraic framework in quantum integrable systems.

Contribution

It constructs a novel dynamical reflection equation algebra and establishes its structure as a right comodule algebra over a dynamical FRT algebra, introducing dynamical trace for central element construction.

Findings

Constructed a dynamical reflection equation algebra $ ilde{ ext{K}}$.

Established $ ilde{ ext{K}}$ as a right comodule algebra over a dynamical FRT algebra.

Introduced dynamical trace and constructed central elements.

Abstract

We construct a dynamical reflection equation algebra, $\tilde {\mathcal{K}}$, via a dynamical twist of the ordinary reflection equation algebra. A dynamical version of the reflection equation is deduced as a corollary. We show that $\tilde {\mathcal{K}}$ is a right comodule algebra over a dynamical analog of the Faddeev-Reshetikhin-Takhtajan algebra equipped with a structure of right bialgebroid. We introduce dynamical trace and use it for constructing central elements of $\tilde {\mathcal{K}}$.