# Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of CYBE

## TL;DR

This paper explores the combinatorial structure of quasi-trigonometric solutions to the classical Yang-Baxter equation derived from simple vector bundles on a nodal Weierstrass cubic, linking algebraic geometry with integrable systems.

## Contribution

It introduces a novel connection between vector bundles on singular cubic curves and solutions to the CYBE, providing new insights into their combinatorial properties.

## Key findings

- Characterization of quasi-trigonometric solutions from vector bundles
- New combinatorial descriptions of CYBE solutions
- Link between algebraic geometry and integrable systems

## Abstract

In this paper we study the combinatorics of quasi-trigonometric solutions of the classical Yang-Baxter equation, arising from simple vector bundles on a nodal Weierstrass cubic.