Root vectors of the composition algebra of the Kronecker algebra - Chen, X. (Algebra and Discrete Mathematics, 2004)
According to the canonical isomorphism between
the positive part Uq⁺(g) of the Drinfeld–Jimbo quantum group
Uq(g) and the generic composition algebra C(∆) of Λ, where the
Kac–Moody Lie algebra g and the finite dimensional hereditary algebra Λ have the same diagram, in specially, we get a realization
of quantum root vectors of the generic composition algebra of the
Kronecker algebra by using the Ringel–Hall approach. The commutation relations among all root vectors are given and an integral
PBW–basis of this algebra is also obtained.