THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H*-ALGEBRA

被引：0

作者：

A.J.Calderón Martín ^{[1
]}

C.Martín González ^{[2
]}

机构：

[1] Departamento de Matemáticas, Universidad de Cádiz

[2] Departamento de Algebra, Geometría y Topología, Universidad de Málaga

来源：

ActaMathematicaScientia | 2010年 / 30卷 / 04期

关键词：

Banach-Lie group; Lie triple automorphism; Lie triple derivation;

D O I：

暂无

中图分类号：

O152.5 [李群];

学科分类号：

070104 ;

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.

引用

页码：1219 / 1226

页数：8

共 50 条

[21] Asymptotic products and enlargibility of Banach-Lie algebras
Beltita, D
JOURNAL OF LIE THEORY, 2004, 14 (01) : 215 - 226
[22] LARGE SCALE GEOMETRY OF BANACH-LIE GROUPS
Ando, Hiroshi
Doucha, Michal
Matsuzawa, Yasumichi
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 375 (04) : 2827 - 2881
[23] On automorphisms and derivations of a Lie algebra
Varea, VR
Varea, JJ
ALGEBRA COLLOQUIUM, 2006, 13 (01) : 119 - 132
[24] Banach-Lie groupoids associated to W*-algebras
Odzijewicz, Anatol
Slizewska, Aneta
JOURNAL OF SYMPLECTIC GEOMETRY, 2016, 14 (03) : 687 - 736
[25] CARTAN SUBALGEBRAS OF BANACH-LIE ALGEBRAS OF OPERATORS
ALAGIA, HR
PACIFIC JOURNAL OF MATHEMATICS, 1982, 98 (01) : 1 - 15
[26] On the smoothness of some quotients of Banach-Lie groups
Beltita, Daniel
Pelletier, Fernand
Zergane, Amel
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2019, 67
[27] A LINEAR APPROACH TO LIE TRIPLE AUTOMORPHISMS OF H*-ALGEBRAS
Calderon Martin, A. J.
Martin Gonzalez, C.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 48 (01) : 117 - 132
[28] THE GROUP OF AUTOMORPHISMS OF THE LIE ALGEBRA OF DERIVATIONS OF A FIELD OF RATIONAL FUNCTIONS
Bavula, V. V.
GLASGOW MATHEMATICAL JOURNAL, 2017, 59 (03) : 513 - 524
[29] On Banach-Lie algebras, spectral decompositions and complex polarizations
Beltita, D
RECENT ADVANCES IN OPERATOR THEORY, OPEATOR ALGEBRAS, AND THEIR APPLICATIONS, 2005, 153 : 13 - 38
[30] Quantum control in infinite dimensions and Banach-Lie algebras
Keyl, Michael
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), 2019, : 2298 - 2303

← 1 2 3 4 5 →