Notes on two-parameter quantum groups, (I)

Abstract

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An operator realization of the positive part is given.

11 pages

References in corpus (3)

• Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
• Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality
• Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis

Cited by in corpus (7)

• Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B
• Notes on two-parameter quantum groups, (II)
• On the Center of Two-parameter Quantum Groups $U_{r,s}({\mathfrak{so}}_{2n+1})$
• Fusion procedure for Yokonuma-Hecke algebras
• Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials
• Novel isoclasses of one-parameter exotic small quantum groups originating from a two-parameter framework
• Harish-Chandra Theorem for Two-parameter Quantum Groups