Right Coideal Subalgebras of Quantized Universal Enveloping Algebras of Type G 2*

Abstract

In this article we describe the right coideal subalgebras containing all group-like elements of the two-parameter quantum group U q (𝔤), where 𝔤 is a simple Lie algebra of type G 2, while the main parameter of quantization q is not a root of 1. As a consequence, we determine that there are precisely 60 different right coideal subalgebras containing all group-like elements. If the multiplicative order t of q is finite, t > 4, t ≠ 6, then the same classification remains valid for homogeneous right coideal subalgebras of the two-parameter version of the small Lusztig quantum group u q (𝔤).