Right Coideal Subalgebras of Quantized Universal Enveloping Algebras of Type G₂*

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).

Key Words:

• Coideal subalgebras
• Hopf algebras
• PBW-generators
• Quantum groups

2000 Mathematics Subject Classification:

• 16W30
• 17B37

ACKNOWLEDGMENTS

I would like to thank professor Kharchenko for all his attention during my research period in Mexico. I also thank him for proposing this theme as part of my thesis and for all his suggestions to this article.

Notes

Communicated by I. Shestakov.

*This article was written based on a research period at the UNAM FES-C, Mexico, with the support of CNPq-Brazil. It is part of the author's PhD thesis.