Leavitt Path Algebra

picture info	Leavitt Path Algebra In mathematics, a Leavitt path algebra is a universal algebra constructed from a directed graph. Leavitt path algebras generalize Leavitt algebras and may be considered as algebraic analogues of graph C-algebras. History Leavitt path algebras were simultaneously introduced in 2005 by Gene Abrams and Gonzalo Aranda Pino as well as by Pere Ara, María Moreno, and Enrique Pardo, with neither of the two groups aware of the other's work. Leavitt path algebras have been investigated by dozens of mathematicians since their introduction, and in 2020 Leavitt path algebras were added to the Mathematics Subject Classification with code 16S88 under the general discipline of Associative Rings and Algebras. The basic reference is the book ''Leavitt Path Algebras''. Graph terminology The theory of Leavitt path algebras uses terminology for graphs similar to that of C-algebraists, which differs slightly from that used by graph theorists. The term graph is typically taken to mean a directed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Universal Algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of studythis is the subject of group theory and ring theory in universal algebra, the object of study is the possible types of algebraic structures and their relationships. Basic idea In universal algebra, an (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. Arity An ''n''- ary operation on ''A'' is a function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a '' constant'', often denoted by a letter like ''a''. A 1-ary operation (or '' unary operation'') is simply a function from ''A'' to ''A'', often denoted by a symbol placed in front of its argument, like ~'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Leavitt Algebra Leavitt may refer to: People Leavitt (surname) Places ;United States Leavitt, California * Leavitt Lake, a lake in Minnesota Leavitt Peak, California Leavitt Township, Michigan Leavittsburg, Ohio Leavittstown, New Hampshire, name later changed to Effingham, New Hampshire ;Canada Leavitt, Alberta ;Extraterrestrial Leavitt (crater) * 5383 Leavitt, asteroid Structures ;United States Leavitt Area High School, Turner, Maine Blazo-Leavitt House, Parsonsfield, Maine James Leavitt House, Waterboro Center, Maine Thomas Leavitt House, Bunkerville, Nevada See also Levett Levett is a surname of Anglo-Normans, Anglo-Norman origin, deriving from eLivet, which is held particularly by families and individuals resident in England and British Commonwealth territories. Origins This surname comes from the village of ... Lovett (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	*Graph C-algebras** In mathematics, a graph C-algebra is a universal C-algebra constructed from a directed graph. Graph C-algebras are direct generalizations of the Cuntz algebras and Cuntz-Krieger algebras, but the class of graph C-algebras has been shown to also include several other widely studied classes of C-algebras. As a result, graph C-algebras provide a common framework for investigating many well-known classes of C-algebras that were previously studied independently. Among other benefits, this provides a context in which one can formulate theorems that apply simultaneously to all of these subclasses and contain specific results for each subclass as special cases. Although graph C-algebras include numerous examples, they provide a class of C-algebras that are surprisingly amenable to study and much more manageable than general C-algebras. The graph not only determines the associated C-algebra by specifying relations for generators, it also provides a useful tool for describing and ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]