Usage
Quasi-Hopf algebras form the basis of the study of Drinfeld twists and the representations in terms of F-matrices associated with finite-dimensional irreducible representations of quantum affine algebra. F-matrices can be used to factorize the corresponding R-matrix. This leads to applications in Statistical mechanics, as quantum affine algebras, and their representations give rise to solutions of the Yang-Baxter equation, a solvability condition for various statistical models, allowing characteristics of the model to be deduced from its corresponding quantum affine algebra. The study of F-matrices has been applied to models such as the Heisenberg XXZ model in the framework of the algebraic Bethe ansatz. It provides a framework for solving two-dimensional integrable models by using the Quantum inverse scattering method.
Read more about this topic: Quasi-Hopf Algebra
Famous quotes containing the word usage:
“...Often the accurate answer to a usage question begins, “It depends.” And what it depends on most often is where you are, who you are, who your listeners or readers are, and what your purpose in speaking or writing is.”
—Kenneth G. Wilson (b. 1923)
“Pythagoras, Locke, Socrates—but pages
Might be filled up, as vainly as before,
With the sad usage of all sorts of sages,
Who in his life-time, each was deemed a bore!
The loftiest minds outrun their tardy ages.”
—George Gordon Noel Byron (1788–1824)
“I am using it [the word ‘perceive’] here in such a way that to say of an object that it is perceived does not entail saying that it exists in any sense at all. And this is a perfectly correct and familiar usage of the word.”
—A.J. (Alfred Jules)