alexa Braided Weyl algebras and differential calculus on U ( u (2))
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Dimitri Gurevich, Pavel Pyatov

Abstract Share this page

On any Reflection Equation algebra corresponding to a skew-invert ible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial Reflection Equation algebra they generate a ”braided analog” of the Weyl algebra. When q → 1, the braided Weyl algebra corresponding to the Quantum Group U q ( sl (2)) goes to the Weyl algebra defined on the algebra Sym(( u (2)) or that U ( u (2)) depending on the way of passing to the limit. Thus, we define partial derivatives on the algebra U ( u (2)), find their ”eigenfunctions”, and introduce an analog of the Laplace operator on this algebra. Also, we define th e ”radial part” of this operator, express it in terms of ”quantum eigenvalues”, and sket ch an analog of the de Rham complex on the algebra U ( u (2)). Eventual applications of our approach are discussed.

  • To read the full article Visit
  • Open Access
This article was published in arXiv.org and referenced in Journal of Generalized Lie Theory and Applications

Recommended Conferences

Relevant Topics

Peer Reviewed Journals
 
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
 
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

 
© 2008-2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version
adwords