| THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H^＊-ALGEBRA^＊ |
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| 引用本文： | A.J.Calderón Martín,C.Martín González.THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H^＊-ALGEBRA^＊[J].数学物理学报(B辑英文版),2010,30(4):1219-1226. |
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| 作者姓名： | A.J.Calderón Martín C.Martín González |
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| 作者单位： | [1]Departamento de Matemáticas, Universidad de Cádiz,11510 Puerto Real, Cádiz, Spain [2]Departamento de lgebra, Geometría y Topología, Universidad de Málaga,Apartado 59, 29080 Málaga, Spain |
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| 基金项目： | the PCI of the UCA 'Teoría de Lie y Teoría de Espacios de Banach' |
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| 摘 要： | We study the Banach-Lie group Ltaut(A) of Lie triple automorphisms of a complex associative H*-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder(A), are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut(A)0 = Aut(A) implying Ltder(A) = Der(A). In the finite-dimensional case Ltaut(A)0 is a direct product of Aut(A) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.
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| 关 键 词： | 李代数 李群 巴拿赫 同构 三联 Banach 无穷维 奥地利 |
| 收稿时间： | 10 November 2007 |
| 修稿时间： | 7 October 2008 |
THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H*-ALGEBRA |
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| A.J.Calderon Martin C. Mart&#;n Gonz&#;lez.THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H*-ALGEBRA[J].Acta Mathematica Scientia,2010,30(4):1219-1226. |
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| Authors: | AJCalderon Martin C Mart&#;n Gonz&#;lez |
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| Institution: | A.J.Calderon Martin C. Martín González |
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| Abstract: | We study the Banach-Lie group Ltaut(A) of Lie triple automorphisms of a complex associative H*-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder(A), are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut(A)0 = Aut(A) implying Ltder(A) = Der(A). In the finite-dimensional case Ltaut(A)0 is a direct product of Aut(A) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators. |
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| Keywords: | Banach-Lie group Lie triple automorphism Lie triple derivation |
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