The structure of Leavitt path algebras and the Invariant Basis Number property |
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| Affiliation: | 1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam;2. Department of Mathematics, FPT University, Hanoi, Vietnam;3. Department of Mathematics Teacher Education, Dong Thap University, Vietnam;1. Department of Mathematics, The University of Texas at Tyler, 3900 University Boulevard, Tyler, TX 75799, United States of America;2. Department of Mathematics, 1400 Stadium Road, University of Florida, Gainesville, FL 32611, United States of America;1. Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand;2. School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia;1. Departament de Matemàtiques, Facultat de Ciències, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain;2. Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80918, USA;1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam;2. Faculty of Computer Science and Mathematics, University of Passau, Germany;1. Tüccarbasi sok. Kaşe apt. No: 10A/25 Erenköy Kadıköy, Istanbul, Turkey;2. Department of Mathematics, Düzce University, Konuralp Düzce, Turkey;3. Department of Mathematics, University of Colorado, Colorado Springs, CO 80919, USA |
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| Abstract: | In this paper, we provide the structure of the Leavitt path algebra of a finite graph via some step-by-step process of source eliminations, and restate Kanuni and Özaydin's nice criterion for Leavitt path algebras of finite graphs having Invariant Basis Number via matrix-theoretic language. Consequently, we give a matrix-theoretic criterion for the Leavitt path algebra of a finite graph having Invariant Basis Number in terms of a sequence of source eliminations. Using these results, we show certain classes of finite graphs for which Leavitt path algebras have Invariant Basis Number, as well as investigate the Invariant Basis Number property of Leavitt path algebras of certain Cayley graphs of finite groups. |
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| Keywords: | Cohn path algebra Invariant Basis Number Leavitt path algebra Cayley and power graphs |
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