The Leavitt path algebra of a graph

For any row-finite graph E and any field K we construct the Leavitt path algebra L ( E ) having coefficients in K. When K is the field of complex numbers, then L ( E ) is the algebraic analog of the Cuntz–Krieger algebra C ∗ ( E ) described in [I. Raeburn, Graph algebras, in: CBMS Reg. Conf. Ser. Ma...

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Bibliographic Details
Published inJournal of algebra Vol. 293; no. 2; pp. 319 - 334
Main Authors Abrams, Gene, Aranda Pino, Gonzalo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.11.2005
Subjects
Cuntz–Krieger [formula omitted]-algebra
Leavitt algebra
Path algebra
Cuntz–Krieger C ∗ -algebra
Path algebra
Leavitt algebra
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Summary:For any row-finite graph E and any field K we construct the Leavitt path algebra L ( E ) having coefficients in K. When K is the field of complex numbers, then L ( E ) is the algebraic analog of the Cuntz–Krieger algebra C ∗ ( E ) described in [I. Raeburn, Graph algebras, in: CBMS Reg. Conf. Ser. Math., vol. 103, Amer. Math. Soc., 2005]. The matrix rings M n ( K ) and the Leavitt algebras L ( 1 , n ) appear as algebras of the form L ( E ) for various graphs E. In our main result, we give necessary and sufficient conditions on E which imply that L ( E ) is simple.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2005.07.028