Reflection equation and twisted Yangians
نویسنده
چکیده
With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given. Applications to the twisted Yangians are considered.
منابع مشابه
Twisted Yangians, Twisted Quantum Loop Algebras and Affine Hecke Algebras of Type Bc
We study twisted Yangians of type AIII which have appeared in the literature under the name of reflection algebras. They admit q-versions which are new twisted quantum loop algebras. We explain how these can be defined equivalently either via the reflection equation or as coideal subalgebras of Yangians of gln (resp. of quantum loop algebras of gln). The connection with affine Hecke algebras of...
متن کاملOn reflection algebras and twisted Yangians
It is known that integrable models associated to rational R matrices give rise to certain non-abelian symmetries known as Yangians. Analogously ‘boundary’ symmetries arise when general but still integrable boundary conditions are implemented, as originally argued by Delius, Mackay and Short from the field theory point of view, in the context of the principal chiral model on the half line. In th...
متن کاملOn reflection algebras and boundary Yangians
It is well known that integrable models associated to rational R matrices give rise to certain non-abelian symmetries called Yangians. An analogous situation arises when general integrable boundary conditions are implemented. In this letter we derive explicitly the generators of the ‘boundary’ Yangians associated to non-diagonal solutions of the reflection equation. LAPTH-1035/04 March 2004 e-m...
متن کاملContracted and expanded integrable structures
We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of boundary integrable models. A quite old paradox concerning the“expansion” of the E2 algebra into sl2 is resolved using the representation theory of the aforementi...
متن کاملTwisted Yangians and symmetric pairs
We describe recent work on the twisted Yangians Y (g,h) which arise as boundary remnants of Yangians Y (g) in 1+1D integrable field theories, bringing out the special role played by the requirement that (g,h) be a symmetric pair.
متن کامل