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Algebras, graphs and their applicati...

Cho, Ilwoo.

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Algebras, graphs and their applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algebras, graphs and their applications // Ilwoo Cho ; edited by Palle E.T.Jorgensen.
作者:	Cho, Ilwoo.
其他作者:	Jørgensen, Palle E. T.,
出版者:	Boca Raton, FL :CRC Press, : 2014.,
面頁冊數:	xii, 431 p. :ill ;24 cm.
標題:	Groupoids. -
ISBN:	9781466590199 (hbk.) :

Algebras, graphs and their applications /
Cho, Ilwoo.

Algebras, graphs and their applications /Ilwoo Cho ; edited by Palle E.T.Jorgensen. - Boca Raton, FL :CRC Press,2014. - xii, 431 p. :ill ;24 cm. - A science publishers book.

Includes bibliographical references and index.

Preface --

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.

ISBN: 9781466590199 (hbk.) :UK63.99

LCCN: 2013011776Subjects--Topical Terms:

708417
Groupoids.

LC Class. No.: QA181 / .C46 2014

Dewey Class. No.: 511/.54

Algebras, graphs and their applications /
LDR:02327cam a2200241 i 4500 001 1931908
003 OCoLC
005 20141117110517.0
008 140826s2014 flu b 001 0 eng
010 $a 2013011776
020 $a 9781466590199 (hbk.) : $c UK63.99
020 $a 146659019X (hbk.)
020 $a 9781466590205 (ebk.)
020 $a 1466590203 (ebk.)
040 $a DLC $b eng
050 0 0 $a QA181 $b .C46 2014
082 0 0 $a 511/.54 $2 23
100 1 $a Cho, Ilwoo. $3 2070319
245 1 0 $a Algebras, graphs and their applications / $c Ilwoo Cho ; edited by Palle E.T.Jorgensen.
260 # $a Boca Raton, FL : $b CRC Press, $c 2014.
300 $a xii, 431 p. : $b ill ; $c 24 cm.
490 1 0 $a A science publishers book
504 $a Includes bibliographical references and index.
505 0 # $t Preface -- $t Algebras on graphs -- $t Representations and operator algebras of graph groupoids -- $t Operator theory on graphs -- $t Fractals on graph groupoids -- $t Entropy theory on graphs -- $t Jones Index Theory on graph groupoids -- $t Network theory on graphs -- $t K-theory on graphs -- $t Index.
520 # $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.
650 # 0 $a Groupoids. $3 708417
650 # 0 $a Operator theory. $3 542531
700 1 # $a Jørgensen, Palle E. T., $d 1947- $3 1575375