The Hom-Yang-Baxter equation and Hom-Lie algebras

Journal Article · Sun May 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3571970· OSTI ID:21501337

Yau, Donald ^[1]

---

1. Department of Mathematics, Ohio State University at Newark, 1179 University Drive, Newark, OH 43055 (United States)

Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.

• OSTI ID: 21501337
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 5; Other Information: DOI: 10.1063/1.3571970; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGEBRA
EQUATIONS
LIE GROUPS
MATHEMATICAL SOLUTIONS
POLYNOMIALS
FUNCTIONS
MATHEMATICS
SYMMETRY GROUPS