Extreme cycles
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line point...
| Authors: | , , , , |
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| Format: | article |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:144968 |
| Online Access: | https://ddd.uab.cat/record/144968 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_60116_09 |
| Access Level: | Open access |
| Keyword: | Leavitt path algebra Center Socle Extreme cycle Cycle Line point |
| Summary: | In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra [13]. We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(Pec ∪ Pc ∪ Pl) generated by vertices in extreme cycles (Pec), by vertices in cycles without exits (Pc), and by line points (Pl) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to Pl ∪ Pc ∪ Pec. Hence its structure will contain much of the information about the Leavitt path algebra. In the row-finite case, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations (Pb∞). |
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