Compact graph C 鈭?/sup>-algebras
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- 作者：G. Aranda聽Pino (1)
D. Mart铆n聽Barquero (2)
C. Mart铆n聽Gonz谩lez (1)
M. Siles聽Molina (1) - 关键词：Compact C 鈭?algebra ; Graph C 鈭?algebra ; Leavitt path algebra ; Socle ; Arbitrary graph ; 16D70 ; 46L55
- 刊名：Revista Matem篓垄tica Complutense
- 出版年：2013
- 出版时间：January 2013
- 年：2013
- 卷：26
- 期：1
- 页码：271-281
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D. Mart铆n聽Barquero (2)
C. Mart铆n聽Gonz谩lez (1)
M. Siles聽Molina (1)
1. Departamento de 脕lgebra, Geometr铆a y Topolog铆a, Universidad de M谩laga, 29071, M谩laga, Spain
2. Departamento de Matem谩tica Aplicada, Universidad de M谩laga, 29071, M谩laga, Spain - ISSN：1988-2807
文摘
We show that compact graph C 鈭?/sup>-algebras C 鈭?/sup>(E) are topological direct sums of finite matrices over 鈩?and KL(H), for some countably dimensional Hilbert space, and give a graph-theoretic characterization as those whose graphs are row-finite, acyclic and every infinite path ends in a sink. We further specialize in the simple case providing both structure and graph-theoretic characterizations. In order to reach our goals we make use of Leavitt path algebras L 鈩?/sub>(E). Moreover, we describe the socle of C 鈭?/sup>(E) as the two-sided ideal generated by the line point vertices.