{"product_id":"operations-on-graphs-groupoids-and-operator-algebras-von-ilwoo-cho","title":"Operations on Graphs, Groupoids, and Operator Algebras","description":"\u003cp\u003eIn this monograph, we consider natural operations on  directed graphs. And we find the connections between  our operations on graphs and the groupoid-perations  on \"graph\" groupoids. Remark that we cannot guarantee the (algebraic or categorial) groupoids  generated by the grouopoid-operations; sum, product,  quotient or complement; of graph groupoids are again  graph groupoids. By defining suitable operations on  graphs, we can conclude the groupoids generated by  the groupoid-operations of graph groupoids are again  graph groupoids; for example, the product groupoid  of two graph groupoids is groupoid-isomorphic to the  graph groupoid of the product graph, etc. This  provides another bridge connceting combinatorics and  algebra. Recently, the von Neumann algebras  generated by graph groupoids, called graph von  Neumann algebras, have been studied. By using the  fundamental techniques from graph von Neumann  algebra theory, we can characterize the properties  of groupoid von Neumann algebras, generated by  groupoids obtained from the groupoid-operations, as  certain graph von Neumann algebras.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838352718\"\u003e\u003ch3\u003eOperations on Graph-Depending Structures\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838352718","offer_id":39499108319325,"sku":"9783838352718","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/1b344982-9bf7-4be0-8c78-069643cbd2e6.jpg?v=1773382786","url":"https:\/\/shop.autorenwelt.de\/en\/products\/operations-on-graphs-groupoids-and-operator-algebras-von-ilwoo-cho","provider":"Autorenwelt Shop","version":"1.0","type":"link"}