A connection between Uq(sl(3)) and Z2×Z2-graded special linear Lie colour algebras via Klein operators

Abstract

We provide an explicit connection between the quantum group Uq(sl(3)) in the limit q → −1 and a Z2×Z2-graded Lie colour algebra. This is realised through an algebra embedding assisted by a Klein operator. This provides a proof of concept of an explicit method that could lead to constructing more general Z2×Z2-graded Lie colour algebras, and their representations.