• Corpus ID: 235669918

The algebra $U^+_q$ and its alternating central extension $\mathcal U^+_q$

@inproceedings{Terwilliger2021TheA,
  title={The algebra \$U^+\_q\$ and its alternating central extension \$\mathcal U^+\_q\$},
  author={Paul M. Terwilliger},
  year={2021}
}
Let U+ q denote the positive part of the quantized enveloping algebra Uq(ŝl2). The algebra U+ q has a presentation involving two generators W0, W1 and two relations, called the q-Serre relations. In 1993 I. Damiani obtained a PBW basis for U+ q , consisting of some elements {Enδ+α0} ∞ n=0, {Enδ+α1} ∞ n=0, {Enδ} ∞ n=1. In 2019 we introduced the alternating central extension U+ q of U + q . We defined U + q by generators and relations. The generators, said to be alternating, are denoted {W−k} ∞ k… 

References

SHOWING 1-10 OF 18 REFERENCES

The alternating central extension for the positive part of Uq(slˆ2)

A compact presentation for the alternating central extension of the positive part of Uq(sl^2)

This paper concerns the positive part U q + of the quantum group U q ( sl ^ 2 ) . The algebra U q + has a presentation involving two generators that satisfy the cubic q -Serre relations. We recently

The alternating PBW basis for the positive part of Uq(sl^2)

The positive part Uq+ of Uq(sl^2) has a presentation with two generators A, B that satisfy the cubic q-Serre relations. We introduce a PBW basis for Uq+, said to be alternating. Each element of this

Quantum affine algebras

AbstractWe classify the finite-dimensional irreducible representations of the quantum affine algebra $$U_q (\hat sl_2 )$$ in terms of highest weights (this result has a straightforward

Introduction to Quantum Groups

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra

Braid group action and quantum affine algebras

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop-like

Groupes quantiques et algèbres de battage quantiques

Soit U q + la sous-algebre de Hopf «triangulaire superieure» de l'algebre enveloppante quantifiee associee a une matrice de Cartan generalisee symetrisable. On montre que U q + est isomorphe a la