The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
By Donald Yau. 2009
162 citations recorded by the source corpus.
We study a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), which is motivated by Hom–Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom–Lie algebras and the others from Drinfeld's (dual) quasi-triangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/277cdb50548ac7b192b7f52fc9c2dfaa76da5006
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In Algebra and Number Theory
- F. Ammar
- Abdenacer Makhlouf
- Donald Yau
- Y. Sheng
- Florin Panaite
- Sergei Silvestrov
- Aron Gohr
- S. Benayadi
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras (2009, methodology): “coassociative coalgebras, Hom-bialgebras and Hom-Hopf algebras (see [18, 20]). It is shown in [24] that the universal enveloping Hom-associative algebra carries a structure of Hom-bialgebra. See also [2, 3, 8, 19, 23, 25, 26] for other works on twisted algebraic structures. This paper focusses on Z2”
- HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS (2009, background): “Hom-associative algebra (see [29]). Dualizing Hom-associative algebras, one can define Hom-coassociative coalgebras, Hom-bialgebras and Hom-Hopf algebras which were introduced in ( [21, 19]), see also [5, 32, 33, 34, 35, 36]. It is shown in [31] that the universal enveloping Hom-associative algebra c”
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “A twisted version of Yang-Baxter equation, quasitriangular bialgebras and quantum groups were discussed in [47, 48, 49, 50, 51].”