Quantization of non-unitary geometric classical $r$-matrices
نویسندگان
چکیده
منابع مشابه
2 00 2 QUANTIZATION OF NON - UNITARY GEOMETRIC CLASSICAL r - MATRICES
In this paper we explicitly attach to a geometric classical r-matrix r (not necessarily unitary), a geometric (i.e., set-theoretical) quantum R-matrix R, which is a quantization of r. To accomplish this, we use the language of bijective cocycle 7-tuples, developed by A. Soloviev in the study of set-theoretical quantum R-matrices. Namely, we define a classical version of bijective cocycle 7-tupl...
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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 (...
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In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed.
متن کامل1 M ar 1 99 9 QUANTIZATION OF GEOMETRIC CLASSICAL r - MATRICES
In this note we define geometric classical r-matrices and quantum Rmatrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed. The idea of the above quantization was inspired by the results in [ESS]. W...
متن کامل2 M ar 1 99 9 QUANTIZATION OF GEOMETRIC CLASSICAL r - MATRICES
In this note we define geometric classical r-matrices and quantum Rmatrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed. The idea of the above quantization was inspired by the results in [ESS]. W...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2005
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2005.v12.n2.a1