The Banach-Lie Group of Lie Automorphisms of an H * -Algebra

Antonio J. Calderón Martín; Candido Martín González

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 623-631
  • ISSN: 0392-4033

Abstract

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We study the Banach-Lie group Aut ( A - ) of Lie automorphisms of a complex associative H * -algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of A , are obtained. For a topologically simple A , in the infinite-dimensional case we have Aut ( A - ) 0 = Aut ( A ) implying Der ( A ) = Der ( A - ) . In the finite dimensional case Aut ( A - ) 0 is a direct product of Aut ( A ) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

How to cite

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Calderón Martín, Antonio J., and Martín González, Candido. "The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 623-631. <http://eudml.org/doc/290408>.

@article{CalderónMartín2007,
abstract = {We study the Banach-Lie group $\operatorname\{Aut\}(A^-)$ of Lie automorphisms of a complex associative $H^*$-algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of $A$, are obtained. For a topologically simple $A$, in the infinite-dimensional case we have $\operatorname\{Aut\}(A^-)_0 = \operatorname\{Aut\}(A)$ implying $\operatorname\{Der\}(A) = \operatorname\{Der\}(A^-)$. In the finite dimensional case $\operatorname\{Aut\}(A^\{-\})_\{0\}$ is a direct product of $\operatorname\{Aut\}(A)$ and a certain subgroup of Lie derivations $\delta$ from $A$ to its center, annihilating commutators.},
author = {Calderón Martín, Antonio J., Martín González, Candido},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {623-631},
publisher = {Unione Matematica Italiana},
title = {The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra},
url = {http://eudml.org/doc/290408},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Calderón Martín, Antonio J.
AU - Martín González, Candido
TI - The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 623
EP - 631
AB - We study the Banach-Lie group $\operatorname{Aut}(A^-)$ of Lie automorphisms of a complex associative $H^*$-algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of $A$, are obtained. For a topologically simple $A$, in the infinite-dimensional case we have $\operatorname{Aut}(A^-)_0 = \operatorname{Aut}(A)$ implying $\operatorname{Der}(A) = \operatorname{Der}(A^-)$. In the finite dimensional case $\operatorname{Aut}(A^{-})_{0}$ is a direct product of $\operatorname{Aut}(A)$ and a certain subgroup of Lie derivations $\delta$ from $A$ to its center, annihilating commutators.
LA - eng
UR - http://eudml.org/doc/290408
ER -

References

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  11. MATHIEU, M. - VILLENA, A. R., Lie and Jordan derivations from Von Neumann Algebras, Preprint. 
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