Twisted Yangians for symmetric pairs of types B, C, D

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan’s classification. These algebras can be regarded as coideal subalgebras of the Yangian for orthogonal or symplectic Lie algebras. They can also be presented as q...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Zeitschrift 2016-10, Vol.284 (1-2), p.131-166
Main Authors: Guay, Nicolas, Regelskis, Vidas
Format: Article
Language:English
Subjects:
Algebra
Lie groups
Mathematics
Mathematics and Statistics
Quotients
Reflection
Symmetry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan’s classification. These algebras can be regarded as coideal subalgebras of the Yangian for orthogonal or symplectic Lie algebras. They can also be presented as quotients of a reflection algebra by additional symmetry relations. We prove an analogue of the Poincaré–Birkoff–Witt Theorem, determine their centres and study also extended reflection algebras.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-016-1649-2