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Algebraic framework for quantization of nonultralocal models. (English) Zbl 0893.17023

Summary: Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang-Baxter-type consistency conditions, as well as conditions for the existence of the multiple coproduct (monodromy matrix), which can be used for construction of the conserved quantities, are given. Homogeneous and local algebras are introduced, and simplification of the Yang-Baxter-type conditions for them is shown. The Yang-Baxter-type equations and multiple coproduct conditions for homogeneous and local of order 2 algebras are solved.

MSC:

17B81 Applications of Lie (super)algebras to physics, etc.
81U40 Inverse scattering problems in quantum theory
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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