Infinite Braided Tensor Products and 2-D quantum Gravity

TL;DR

This paper explores infinite braided tensor products of quantum groups and algebras, showing their relevance to 2D quantum gravity and extending the mathematical framework of braided systems.

Contribution

It introduces the use of infinite braided tensor products to model exchange algebra in 2D quantum gravity, connecting braided tensor structures with physical theories.

Findings

Infinite braided tensor products describe exchange algebra in 2D quantum gravity.

The structure extends to quantum groups and braided groups.

Provides a systematic approach to covariant interactions in quantum systems.

Abstract

Braided tensor products have been introduced by the author as a systematic way of making two quantum-group-covariant systems interact in a covariant way, and used in the theory of braided groups. Here we study infinite braided tensor products of the quantum plane (or other constant Zamolodchikov algebra). It turns out that such a structure precisely describes the exchange algebra in 2D quantum gravity in the approach of Gervais. We also consider infinite braided tensor products of quantum groups and braided groups.