The Connection between Der(<inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold">U</mi><mi mathvariant="bold">q</mi><mo mathvariant="bold">+</mo></msubsup><mrow><mo mathvariant="bold">(</mo><mi mathvariant="bold">g</mi><mo mathvariant="bold">)</mo></mrow></mrow></semantics></math></inline-formula>) and Der(<inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold">U</mi><mrow><mi mathvariant="bold">r</mi><mo mathvariant="bold">,</mo><mi mathvariant="bold">s</mi></mrow><mo mathvariant="bold">+</mo></msubsup><mrow><mo mathvariant="bold">(</mo><mi mathvariant="bold">g</mi><mo mathvariant="bold">)</mo></mrow></mrow></semantics></math></inline-formula>)

Abstract

To facilitate the parallel development of the structures and properties of two-parameter quantum groups with those of one-parameter quantum groups, this paper primarily elucidates the interrelations and distinctions between the derivation algebras of these two types of quantum groups. Additionally, we also proposed a method for deriving the derivation algebra of one-parameter quantum groups from known two-parameter quantum group derivations, and vice versa.

Keywords

• two-parameter quantum groups
• one-parameter quantum groups
• iterated Ore extension
• derivations