Noncommutative String Theory, the R-Matrix, and Hopf Algebras

TL;DR

This paper explores the algebraic structures underlying noncommutative string theory, specifically using R-matrices and Hopf algebras to define deformed multiplication operations that generalize the noncommutative *-product.

Contribution

It introduces a Hopf algebraic framework for noncommutative string theory by defining a deformed multiplication via R-matrices, connecting string theory with algebraic structures.

Findings

The noncommutative *-product arises as a specific case of the deformed multiplication.

The paper establishes properties of the deformed multiplication within quasitriangular Hopf algebras.

It suggests potential algebraic foundations for noncommutative string theory.

Abstract

Motivated by the form of the noncommutative *-product in a system of open strings and Dp-branes with constant nonzero Neveu-Schwarz 2-form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its R-matrix, and comment on some of its properties. We show that the noncommutative string theory *-product is a particular example of this multiplication, and comment on other possible Hopf algebraic properties which may underlie the theory.