# Quantum torus algebras and B(C) type Toda systems

## TL;DR

This paper introduces a new constrained B(C) type Toda hierarchy, explores its symmetries, and generalizes it to an N-component system with symmetries linked to quantum torus algebra structures.

## Contribution

It constructs a novel even constrained B(C) type Toda hierarchy and extends it to an N-component version with associated quantum torus algebra symmetries.

## Key findings

- New B(C) type Toda hierarchy constructed
- Derived B(C) type Block type additional symmetry
- Generalized to N-component hierarchy with quantum torus algebra symmetries

## Abstract

In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is proved to have symmetries of a coupled $\bigotimes^NQT_+ $ algebra ( $N$-folds direct product of the positive half of the quantum torus algebra $QT$).