Confluence and quantum Yang-Baxter equation
نویسندگان
چکیده
منابع مشابه
Finite Groups and Quantum Yang-baxter Equation
The solvability of many 2d lattice statistical models is closely connected to the Quantum Yang-Baxter equation (QYBE) [1, 2]. Solutions of the QYBE are equivalent to weight functions of vertex models. Probably the most simple 2d integrable system is (lattice) gauge theory. The weights of the field configurations around a plaquette satisfy the QYBE Fig.1a. (The gauge group is assumed to be finit...
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The self-dual concept of a quantum quasigroup offers a far-reaching unification of Hopf algebras (along with their non-associative extensions, e.g., [1–4]) and quasigroups [5]. Consider a bimagma (A,∇, ∆), an object of a strict symmetric monoidal category V with V-morphisms giving a magma structure or multiplication ∇ : A⊗ A→ A, and a comagma structure or comultiplication ∆ : A→ A⊗ A, such that...
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Quantum mechanics has had an important influence on building computers; nowadays, quantum mechanics principles are used for the processing and transmission of information. The Yang-Baxter equation is related to the universal gates from quantum computing and it realizes a unification of certain non-associative structures. Unifying structures could be seen as structures which comprise the informa...
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We develop a categorical approach to the dynamical Yang-Baxter equation (DYBE) for arbitrary Hopf algebras. In particular, we introduce a notion of dynamical extension of a monoidal category, which provides a natural environment for quantum dynamical R-matrices. In this context, we define dynamical associative algebras and show that such algebras give a quantization of vector bundles on coadjoi...
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We present solutions of the Quantum Yang-Baxter Equation that satisfy the condition R ab cd 6 = 0) (fa; bg = fc; dg) or (b = (a) and d = (c)); where denotes the involution on f1; : : : ; ng given by (i) = n + 1 ? i.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2000
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(98)00102-9