Right Coideal Subalgebras of the Quantum Borel Algebra of type G2

TL;DR

This paper classifies right coideal subalgebras containing all group-like elements in the quantum Borel algebra of type G2, extending to the small Lusztig quantum group under certain conditions on the parameter q.

Contribution

It provides a detailed classification of right coideal subalgebras in the quantum Borel algebra of type G2, including the multiparameter case and conditions for the small quantum group.

Findings

Classification of right coideal subalgebras containing all group-like elements.

Extension of classification to the small Lusztig quantum group for certain parameters.

Results hold when the main quantization parameter q is not a root of 1.

Abstract

In this paper we describe the right coideal subalgebras containing all group-like elements of the multiparameter quantum group Uq+(g), where g is a simple Lie algebra of type G2, while the main parameter of quantization q is not a root of 1. If the multiplicative order t of q is finite, t>4, t different from 6, then the same classification remains valid for homogeneous right coideal subalgebras of the positive part uq+(g) of the multiparameter version of the small Lusztig quantum group.