PBW-deformations of quantum groups

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文摘

In this paper, we investigate certain deformations B_q(g)

B_{q} (g)

of the negative part

U_{q}^{-} (g)

of quantized enveloping algebras U_q(g)

U_{q} (g)

. An algorithm is established to determine when a given B_q(g)

B_{q} (g)

is a PBW-deformation of

U_{q}^{-} (g)

. For g

g

of type A₂

A_{2}

and B₂

B_{2}

, we classify PBW-deformations of

U_{q}^{-} (g)

. Moreover, we explicitly construct some PBW bases for a class of PBW-deformations B_q(g)

B_{q} (g)

U_{q}^{-} (g)

. As an application, Iorgov–Klimyk's PBW bases for the non-standard quantum deformation

U_{q}^{'} (so (n, C))

of the universal enveloping algebra U(so(n,C))

U (so (n, C))

are recovered.