• Corpus ID: 235669918

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

  title={The algebra \$U^+\_q\$ and its alternating central extension \$\mathcal U^+\_q\$},
  author={Paul M. Terwilliger},
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… 



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 groups and quantum shuffles

Abstract. Let Uq+ be the “upper triangular part” of the quantized enveloping algebra associated with a symetrizable Cartan matrix. We show that Uq+ is isomorphic (as a Hopf algebra) to the subalgebra

An Algebraic Characterization of the Affine Canonical Basis

The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicit

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

A New Current Algebra and the Reflection Equation

We establish an explicit algebra isomorphism between the quantum reflection algebra for the $${U_q(\widehat{sl_2}) R}$$-matrix and a new type of current algebra. These two algebras are shown to be

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