The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
نویسندگان
چکیده
منابع مشابه
ar X iv : 0 90 6 . 41 28 v 1 [ m at h - ph ] 2 2 Ju n 20 09 HOM - QUANTUM GROUPS I : QUASI - TRIANGULAR HOM - BIALGEBRAS
We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel’d’s quasitriangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel’d’s quantum env...
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We construct a Hom-bialgebra M(2) representing the functor of 2 × 2-matrices on Hom-associative algebras. We also construct a Hom-algebra analogue of the affine plane and show that it is a comodule Hom-algebra over M(2) in a suitable sense.
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Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann-Schwarzbach. This approach provides a definition of an L∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L∞-algebra structure as...
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متن کاملQuasi-triangular structures on Hopf algebras with positive bases
A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi triangular structure R ∈ H ⊗ H is said to be positive with respect to B if it has non-negative coefficients in the basis B ⊗ B of H ⊗ H. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper,...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2009
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/42/16/165202