TeX files
This commit is contained in:
Pawel
202
Unitary groups, K-theory and traces/unitary_group_homs.bbl
Normal file
202
Unitary groups, K-theory and traces/unitary_group_homs.bbl
Normal file
@@ -0,0 +1,202 @@
|
||||
\newcommand{\etalchar}[1]{$^{#1}$}
|
||||
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
|
||||
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
|
||||
% \MRhref is called by the amsart/book/proc definition of \MR.
|
||||
\providecommand{\MRhref}[2]{%
|
||||
\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
|
||||
}
|
||||
\providecommand{\href}[2]{#2}
|
||||
\begin{thebibliography}{ARBG12}
|
||||
|
||||
\bibitem[AM03]{AraMathieubook}
|
||||
Pere Ara and Martin Mathieu, \emph{Local multipliers of {C}*-algebras},
|
||||
Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London,
|
||||
2003. \MR{1940428}
|
||||
|
||||
\bibitem[ARBG12]{AlBoothGiordano12}
|
||||
Ahmed Al-Rawashdeh, Andrew Booth, and Thierry Giordano, \emph{Unitary groups as
|
||||
a complete invariant}, J. Funct. Anal. \textbf{262} (2012), no.~11,
|
||||
4711--4730. \MR{2913684}
|
||||
|
||||
\bibitem[Boo98]{Booth98}
|
||||
Andrew Booth, \emph{The unitary group as a complete invariant for simple unital
|
||||
{AF} algebras}, Master's thesis, University of Ottawa (Canada), 1998.
|
||||
|
||||
\bibitem[Bre93]{Bresar93}
|
||||
Matej Bre\v{s}ar, \emph{Commuting traces of biadditive mappings,
|
||||
commutativity-preserving mappings and {L}ie mappings}, Trans. Amer. Math.
|
||||
Soc. \textbf{335} (1993), no.~2, 525--546. \MR{1069746}
|
||||
|
||||
\bibitem[CET{\etalchar{+}}21]{CETWW21}
|
||||
Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White, and Wilhelm
|
||||
Winter, \emph{Nuclear dimension of simple {C}*-algebras}, Invent. Math.
|
||||
\textbf{224} (2021), no.~1, 245--290. \MR{4228503}
|
||||
|
||||
\bibitem[CGS{\etalchar{+}}23]{CGSTW23}
|
||||
Jos{\'e}~R. Carri{\'o}n, James Gabe, Christopher Schafhauser, Aaron Tikuisis,
|
||||
and Stuart White, \emph{Classifying *-homomorphisms {I}: Unital simple
|
||||
nuclear {C}*-algebras}, arXiv:2307.06480 (2023).
|
||||
|
||||
\bibitem[Con85]{Conway19}
|
||||
John~B. Conway, \emph{A course in functional analysis}, Graduate Texts in
|
||||
Mathematics, vol.~96, Springer-Verlag, New York, 1985. \MR{768926}
|
||||
|
||||
\bibitem[CP79]{CuntzPedersen79}
|
||||
Joachim Cuntz and Gert~K. Pedersen, \emph{Equivalence and traces on
|
||||
{C}*-algebras}, Journal of Functional Analysis \textbf{33} (1979), no.~2,
|
||||
135--164.
|
||||
|
||||
\bibitem[CR23]{ChandRobert23}
|
||||
Abhinav Chand and Leonel Robert, \emph{Simplicity, bounded normal generation,
|
||||
and automatic continuity of groups of unitaries}, Adv. Math. \textbf{415}
|
||||
(2023), Paper No. 108894, 52. \MR{4543451}
|
||||
|
||||
\bibitem[Dad95]{Dadarlat95}
|
||||
Marius Dadarlat, \emph{Reduction to dimension three of local spectra of real
|
||||
rank zero {C}*-algebras}, J. Reine Angew. Math. \textbf{460} (1995),
|
||||
189--212. \MR{1316577}
|
||||
|
||||
\bibitem[dlH13]{dlHarpe13}
|
||||
Pierre de~la Harpe, \emph{Fuglede--{K}adison determinant: theme and
|
||||
variations}, Proc. Natl. Acad. Sci. USA \textbf{110} (2013), no.~40,
|
||||
15864--15877. \MR{3363445}
|
||||
|
||||
\bibitem[dlHS84a]{dlHS84a}
|
||||
Pierre de~la Harpe and Georges Skandalis, \emph{D\'{e}terminant associ\'{e} \`a
|
||||
une trace sur une alg\'{e}bre de {B}anach}, Ann. Inst. Fourier (Grenoble)
|
||||
\textbf{34} (1984), no.~1, 241--260. \MR{743629}
|
||||
|
||||
\bibitem[dlHS84b]{dlHS84b}
|
||||
\bysame, \emph{Produits finis de commutateurs dans les {C}*-alg\`ebres}, Ann.
|
||||
Inst. Fourier (Grenoble) \textbf{34} (1984), no.~4, 169--202. \MR{766279}
|
||||
|
||||
\bibitem[Dye53]{Dye53}
|
||||
H.~A. Dye, \emph{The unitary structure in finite rings of operators}, Duke
|
||||
Math. J. \textbf{20} (1953), 55--69. \MR{52695}
|
||||
|
||||
\bibitem[Dye55]{Dye55}
|
||||
\bysame, \emph{On the geometry of projections in certain operator algebras},
|
||||
Ann. of Math. (2) \textbf{61} (1955), 73--89. \MR{66568}
|
||||
|
||||
\bibitem[EGLN15]{EGLN15}
|
||||
George~A. Elliott, Guihua Gong, H.~Lin, and Zhuang Niu, \emph{On the
|
||||
classification of simple amenable {C}*-algebras with finite decomposition
|
||||
rank, {II}}, arXiv:1507.03437 (2015).
|
||||
|
||||
\bibitem[Fol16]{Follandbook16}
|
||||
Gerald~B. Folland, \emph{A course in abstract harmonic analysis}, second ed.,
|
||||
Textbooks in Mathematics, CRC Press, Boca Raton, FL, 2016. \MR{3444405}
|
||||
|
||||
\bibitem[GLN20a]{GongLinNiu20I}
|
||||
Guihua Gong, Huaxin Lin, and Zhuang Niu, \emph{A classification of finite
|
||||
simple amenable $\mathcal{Z}$-stable {C}*-algebras, {I}: {C}*-algebras with
|
||||
generalized tracial rank one}, C. R. Math. Acad. Sci. Soc. R. Can.
|
||||
\textbf{42} (2020), no.~3, 63--450. \MR{4215379}
|
||||
|
||||
\bibitem[GLN20b]{GongLinNiu20II}
|
||||
\bysame, \emph{A classification of finite simple amenable $\mathcal{Z}$-stable
|
||||
{C}*-algebras, {II}: {C}*-algebras with rational generalized tracial rank
|
||||
one}, C. R. Math. Acad. Sci. Soc. R. Can. \textbf{42} (2020), no.~4,
|
||||
451--539. \MR{4215380}
|
||||
|
||||
\bibitem[Gon97]{Gong97}
|
||||
Guihua Gong, \emph{On inductive limits of matrix algebras over
|
||||
higher-dimensional spaces. {I}, {II}}, Math. Scand. \textbf{80} (1997),
|
||||
no.~1, 41--55, 56--100. \MR{1466905}
|
||||
|
||||
\bibitem[Goo86]{Goodearlbook}
|
||||
Kenneth~R. Goodearl, \emph{Partially ordered abelian groups with
|
||||
interpolation}, Mathematical Surveys and Monographs, vol.~20, American
|
||||
Mathematical Society, Providence, RI, 1986. \MR{845783}
|
||||
|
||||
\bibitem[GS16]{GiordanoSierakowski16}
|
||||
Thierry Giordano and Adam Sierakowski, \emph{The general linear group as a
|
||||
complete invariant for {C}*-algebras}, J. Operator Theory \textbf{76} (2016),
|
||||
no.~2, 249--269. \MR{3552377}
|
||||
|
||||
\bibitem[Hal15]{HallBook}
|
||||
Brian Hall, \emph{Lie groups, {L}ie algebras, and representations}, second ed.,
|
||||
Graduate Texts in Mathematics, vol. 222, Springer, Cham, 2015, An elementary
|
||||
introduction. \MR{3331229}
|
||||
|
||||
\bibitem[HM14]{HatoriMolnar14}
|
||||
Osamu Hatori and Lajos Moln\'{a}r, \emph{Isometries of the unitary groups and
|
||||
{T}hompson isometries of the spaces of invertible positive elements in
|
||||
{C}*-algebras}, J. Math. Anal. Appl. \textbf{409} (2014), no.~1, 158--167.
|
||||
\MR{3095026}
|
||||
|
||||
\bibitem[Jia97]{Jiang97}
|
||||
Xinhui Jiang, \emph{Nonstable {K}-theory for $\mathcal{Z}$-stable
|
||||
{C}*-algebras}, arXiv preprint math/9707228 (1997).
|
||||
|
||||
\bibitem[Ng14]{Ng14}
|
||||
Ping~W. Ng, \emph{The kernel of the determinant map on certain simple
|
||||
{C}*-algebras}, J. Operator Theory \textbf{71} (2014), no.~2, 341--379.
|
||||
\MR{3214642}
|
||||
|
||||
\bibitem[NR17]{NgRobert17}
|
||||
Ping~W. Ng and Leonel Robert, \emph{The kernel of the determinant map on pure
|
||||
{C}*-algebras}, Houston J. Math. \textbf{43} (2017), no.~1, 139--168.
|
||||
\MR{3647937}
|
||||
|
||||
\bibitem[Pat83]{Paterson83}
|
||||
Alan L.~T. Paterson, \emph{Harmonic analysis on unitary groups}, J. Funct.
|
||||
Anal. \textbf{53} (1983), no.~3, 203--223. \MR{724026}
|
||||
|
||||
\bibitem[Pau02]{Paulsenbook}
|
||||
Vern Paulsen, \emph{Completely bounded maps and operator algebras}, Cambridge
|
||||
Studies in Advanced Mathematics, vol.~78, Cambridge University Press,
|
||||
Cambridge, 2002. \MR{1976867}
|
||||
|
||||
\bibitem[Phi92]{Phillips92}
|
||||
N.~Christopher Phillips, \emph{The rectifiable metric on the space of
|
||||
projections in a {C}*-algebra}, Internat. J. Math. \textbf{3} (1992), no.~5,
|
||||
679--698. \MR{1189681}
|
||||
|
||||
\bibitem[Phi00]{Phillips00}
|
||||
\bysame, \emph{A classification theorem for nuclear purely infinite simple
|
||||
{C}*-algebras}, Doc. Math. \textbf{5} (2000), 49--114. \MR{1745197}
|
||||
|
||||
\bibitem[Rie87]{Rieffel87}
|
||||
Marc~A. Rieffel, \emph{The homotopy groups of the unitary groups of
|
||||
noncommutative tori}, J. Operator Theory \textbf{17} (1987), no.~2, 237--254.
|
||||
\MR{887221}
|
||||
|
||||
\bibitem[RLL00]{RordamKBook}
|
||||
Mikael R{\o}rdam, Flemming Larsen, and Niels~J. Laustsen, \emph{An introduction
|
||||
to {K}-theory for {C}*-algebras}, London Mathematical Society Student Texts,
|
||||
vol.~49, Cambridge University Press, Cambridge, 2000. \MR{1783408}
|
||||
|
||||
\bibitem[R{\o}r02]{RordamBook}
|
||||
Mikael R{\o}rdam, \emph{Classification of nuclear, simple {C}*-algebras},
|
||||
Classification of nuclear {C}*-algebras. {E}ntropy in operator algebras,
|
||||
Encyclopaedia Math. Sci., vol. 126, Springer, Berlin, 2002, pp.~1--145.
|
||||
\MR{1878882}
|
||||
|
||||
\bibitem[Sak55]{Sakai55}
|
||||
Sh\^{o}ichir\^{o} Sakai, \emph{On the group isomorphism of unitary groups in
|
||||
{AW}*-algebras}, Tohoku Math. J. (2) \textbf{7} (1955), 87--95. \MR{73139}
|
||||
|
||||
\bibitem[Sak12]{Sakaibook}
|
||||
\bysame, \emph{{C}*-algebras and {W}*-algebras}, Springer Science \& Business
|
||||
Media, 2012.
|
||||
|
||||
\bibitem[Sch84]{SchochetIV}
|
||||
Claude Schochet, \emph{Topological methods for {C}*-algebras. {IV}. {M}od {$p$}
|
||||
homology}, Pacific J. Math. \textbf{114} (1984), no.~2, 447--468. \MR{757511}
|
||||
|
||||
\bibitem[Tho93]{Thomsen93}
|
||||
Klaus Thomsen, \emph{Finite sums and products of commutators in inductive limit
|
||||
{C}*-algebras}, Ann. Inst. Fourier (Grenoble) \textbf{43} (1993), no.~1,
|
||||
225--249. \MR{1209702}
|
||||
|
||||
\bibitem[Tho95]{Thomsen95}
|
||||
\bysame, \emph{Traces, unitary characters and crossed products by
|
||||
{$\mathbb{Z}$}}, Publ. Res. Inst. Math. Sci. \textbf{31} (1995), no.~6,
|
||||
1011--1029. \MR{1382564}
|
||||
|
||||
\bibitem[Yen56]{Yen56}
|
||||
Ti~Yen, \emph{Isomorphism of unitary groups in {AW}*-algebras}, Tohoku Math. J.
|
||||
(2) \textbf{8} (1956), 275--280. \MR{89376}
|
||||
|
||||
\end{thebibliography}
|
||||
Reference in New Issue
Block a user