量子环面上一类李代数的导子和中心扩张

曾波;

数学学报 ›› 2009 ›› Issue (01) : 165-172.

中国科学院数学与系统科学研究院期刊网
数学学报 ›› 2009 ›› Issue (01) : 165-172. DOI: 10.12386/A2009sxxb0017
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量子环面上一类李代数的导子和中心扩张

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

    Bo ZENG School of Mathematical Science,Xiangtan University,Xiangtan 411105,P.R.China School of Mathematical Science,Xiamen University,Xiamen 361005,P.R.China
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摘要

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.

Abstract

Let(q):=C_q[x_1~(±1),x=_2~(±1)]Der_(skew)(C_q),where C_q:=C_q[x_1~(±1),x_2~(±1)]is the quantum torus in two variables,Der_(skew)(C_q)is the skew derivation Lie algebra over C_q, and q is any nonzero complex number.Denote L(q)the derived subalgebra[■(q),■(q)] of L(q).In this paper,we determine the derivations and central extensions of L(q) with q a p-th primitive root of unity when p>1.

关键词

量子环面 / 中心扩张 / 导子

Key words

central extension / quantum torus / derivation

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曾波;. 量子环面上一类李代数的导子和中心扩张. 数学学报, 2009(01): 165-172 https://doi.org/10.12386/A2009sxxb0017
Bo ZENG School of Mathematical Science,Xiangtan University,Xiangtan 411105,P.R.China School of Mathematical Science,Xiamen University,Xiamen 361005,P.R.China. The Derivations and Central Extensions of a Class of Lie Algebras over Quantum Torus. Acta Mathematica Sinica, Chinese Series, 2009(01): 165-172 https://doi.org/10.12386/A2009sxxb0017

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