Explicit coproduct formula for quantum group of the type $G_2$

TL;DR

This paper derives an explicit coproduct formula for PBW-generators of the two-parameter quantum group of type G_2, extending known formulas for other Lie algebra types.

Contribution

It provides the first explicit coproduct formula for the quantum group of type G_2, filling a gap in the understanding of its algebraic structure.

Findings

Explicit coproduct formula for G_2 quantum group PBW-generators

Extension of known formulas to the exceptional Lie algebra type G_2

Facilitates further algebraic and representation-theoretic studies of G_2 quantum groups

Abstract

We find a coproduct formula in the explicit form for PBW-generators of the two-parameter quantum group $U_q^+(\frak{g})$ where $\frak{g}$ is a simple Lie algebra of type $G_2$. The similar formulas for quantizations of simple Lie algebras of infinite series are already known.