Heisenberg李(超)代数的自同构群
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摘要
本文研究了Heisenberg李(超)代数的自同构群.利用Heisenberg李(超)代数与线性李(超)代数之间的同构,获得了Heisenberg李(超)代数的自同构群的子群,包括内自同构群、中心自同构群、对合自同构群.
In this paper, we study the automorphism groups of Heisenberg Lie(super)algebras. By using the isomorphisms between Heisenberg Lie(super)algebras and linear Lie(super)algebras, subgroups of automorphism groups of Heisenberg Lie(super)algebras are obtained,including inner automorphism groups, central automorphism groups, involutionary automorphism groups.
In this paper, we study the automorphism groups of Heisenberg Lie(super)algebras. By using the isomorphisms between Heisenberg Lie(super)algebras and linear Lie(super)algebras, subgroups of automorphism groups of Heisenberg Lie(super)algebras are obtained,including inner automorphism groups, central automorphism groups, involutionary automorphism groups.
引文
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[3]Skldberg E.The homology of Heisenberg Lie algebras over fields of characteristic two[J].Math.Proc.R.Ir.Acad.,2005,150(2):47–49.
[4]Rodr?guez-Vallarte M C,Salgado G,S′anchez-Valenzuela O A.Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms[J].J.Alg.,2011,332(1):71–86.
[5]Liu Wende,Chen Meiwei.The minimal dimensions of faithful representations for Heisenberg Lie superalgebras[J].J.Geom.Phys.,2015,89:17–24.
[6]Cao Youan,Tan Zuowen.Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring[J].Linear Alg.Appl.,2003,360:105–122.
[7]张海山,邵文武,卢才辉.Heisenberg李代数的自同构群[J].首都师范大学学报(自然科学版),2007,28(1):1–14.
[2]Jang Cuibo.The holomorph and derivation algebra of infinite dimensional Heisenberg algebra[J].J.Math.,1997,17(3):422–426.
[3]Skldberg E.The homology of Heisenberg Lie algebras over fields of characteristic two[J].Math.Proc.R.Ir.Acad.,2005,150(2):47–49.
[4]Rodr?guez-Vallarte M C,Salgado G,S′anchez-Valenzuela O A.Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms[J].J.Alg.,2011,332(1):71–86.
[5]Liu Wende,Chen Meiwei.The minimal dimensions of faithful representations for Heisenberg Lie superalgebras[J].J.Geom.Phys.,2015,89:17–24.
[6]Cao Youan,Tan Zuowen.Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring[J].Linear Alg.Appl.,2003,360:105–122.
[7]张海山,邵文武,卢才辉.Heisenberg李代数的自同构群[J].首都师范大学学报(自然科学版),2007,28(1):1–14.