Classical quasi-trigonometric r-matrices of Cremmer-Gervais type and their quantization
نویسندگان
چکیده
منابع مشابه
Quantum seaweed algebras and quantization of affine Cremmer–Gervais r-matrices
We propose a method of quantization of certain Lie bialgebra structures on the polynomial Lie algebras related to quasi-trigonometric solutions of the classical Yang–Baxter equation. The method is based on an affine realization of certain seaweed algebras and their quantum analogues. We also propose a method of ω-affinization, which enables us to quantize rational r-matrices of sl(3).
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We describe a quantum Lie algebra based on the Cremmer-Gervais R-matrix. The algebra arises upon a restriction of an infinite-dimensional quantum Lie algebra.
متن کاملGenerating Functions for the Coefficients of the Cremmer-gervais R-matrices
The coefficients of certain operators on V ⊗V can be constructed using generating functions. Necessary and sufficient conditions are given for some such operators to satisfy the Yang-Baxter equation. As a corollary we obtain a simple, direct proof that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation. This approach also clarifies Cremmer and Gervais’s original proof via the dynam...
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If a classical r-matrix r is skewsymmetric, its quantization R can lose the skewsymmetry property. Even when R is skewsymmetric, it may not be unique. Let r be a classical r-matrix. In general, it means that we have a family of vector spaces {Vα}, α ∈ A, and a collection of linear operators r(α, β) : Vα ⊗ Vβ → Vβ ⊗ Vα, ∀ α 6= β ∈ A, (1) satisfying the misnamed “Classical Yang-Baxter” equation (...
متن کامل2 2 Ja n 20 05 Semi - classical twists for sl 3 and sl 4 boundary r − matrices of Cremmer - Gervais type
We obtain explicit formulas for the semi-classical twists deforming coalgebraic structure of U(sl3) and U(sl4). In the rank 2 or 3 the corresponding universal R−matrices quantize the boundary r−matrices of Cremmer-Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in sln.
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ژورنال
عنوان ژورنال: Journal of Non-linear Mathematical Physics
سال: 2006
ISSN: 1402-9251
DOI: 10.2991/jnmp.2006.13.supplement.14