02386cam a2200289 i 450000100090000000300090000900500170001800800410003501000170007602000290009304000280012204200080015005000210015808200160017908400340019510000160022924501930024526000370043830000290047550400510050452013160055565000150187165000210188665000460190765000480195385600950200117725833KE-MeUCS20210128112732.0130506s2014    flu      b    001 0 eng    a  2013011776  a9781466590199 (hardback)  aDLCbengcDLCerdadDLC  apcc00aQA181b.C46 201400a511/.54223  aMAT002000aMAT0370002bisacsh1 aCho, Ilwoo.10aAlgebras, graphs and their applications /cIlwoo Cho, Department of Mathmatics, St. Ambros University, Davenport, Iowa, USA ; edited by Palle E. T. Jorgensen, University of Iowa City, USA.  aNew York:bCRC Press Inc;c2014.  axii, 431 pages ;c24 cm.  aIncludes bibliographical references and index.  a"Preface In this book, we consider algebra on directed graphs. From combinatorial objects, direct graphs, we establish corresponding algebraic objects which become groupoids. We call such groupoids graph groupoids. Connected with groupoid theory, we investigate the properties of graph groupoids. From this investigation, we can realize that graph groupoids act like the free groups in group theory. In other words, the study of graph groupoids is understood as groupoidal version of free-group theory. As application, we observe how graph groupoids are playing their role in different mathematical and scientific areas, including general groupoid theory, representation theory, automata theory, operator algebra (von Neumann algebra theory, C*-algebra theory, free probability, and index theory), noncommutative dynamical systems (groupoid dynamical systems), operator theory (spectral theory), fractal theory, information theory (entropy theory), and network theory, etc. We can check all operated groupoids (for instance, groupoid sums, product groupoids, quotient groupoids, etc) of graph groupoids are graph groupoids, too. This means that the study of operated groupoids of graph groupoids becomes nothing but studying other graph groupoids. It makes us easy to handle graph-groupoid related structures"-- 0aGroupoids. 0aOperator theory. 7aMATHEMATICS / Algebra / General.2bisacsh 7aMATHEMATICS / Functional Analysis.2bisacsh423Cover imageuhttp://images.tandf.co.uk/common/jackets/websmall/978146659/9781466590199.jpg