# Algebraic structure of classical integrability for complex sine-Gordon

### Submission summary

 As Contributors: Luc FRAPPAT Arxiv Link: https://arxiv.org/abs/1911.06720v1 Date submitted: 2019-11-19 Submitted by: FRAPPAT, Luc Submitted to: SciPost Physics Discipline: Physics Subject area: Mathematical Physics Approach: Theoretical

### Abstract

The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1911.06720v1 on 19 November 2019