Borel Subalgebras of the Witt Algebra  

作　　者：Yu Feng YAO Hao CHANG 

机构地区：[1]Department of Mathematics, Shanghai Maritime University [2]Department of Mathematics, East China Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第8期1348-1358,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11201293 and 11271130);the Innovation Program of Shanghai Municipal Education Commission(Grant Nos.13YZ077 and 12ZZ038)

摘　　要：Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.

关 键 词：Witt algebra Borel subalgebra nilpotent element nilpotent cone automorphism group 

分 类 号：O153[理学—数学]