量子环面上一类李代数的导子和中心扩张

The Derivations and Central Extensions of a Class of Lie Algebras over Quantum Torus

设■(q):=C_q[x_1^(±1),x_2^(±1)] Der_(skew)(C_q),其中C_q:=C_q[x_1^(±1),x_2^(±1)]是两个变量的量子环面,Der_(skew)(C_q)是C_q上的斜导子李代数,q是任意非零复数.记■(q)的导代数[■(q),■(q)]为L(q).本文确定了当q是p(>1)次本原单位根时,L(q)的导子和中心扩张.

Let L（q）：= =Cq[x1^±1,x2^±1]＋ Derskew（Cq）, where Cq ：=Cq[x1^±1,x2^±1] quantum torus in two variables, Derskew（Cq） is the skew derivation Lie algebra and q is any nonzero complex number. Denote L（q） the derived subalgebra [L（ of L（q）. In this paper, we determine the derivations and central extensions with q a p-th primitive root of unity when p 〉 1.