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oai:riuma.uma.es:10630/305842026-02-03T11:28:55Zcom_10630_2254col_10630_37953

Leavitt path algebras of Cayley graphs C_n^j. Abrams, Gene Erickson, Stefan Gil-Canto, Cristóbal Sucesiones (Matemáticas) Álgebra Let n be a positive integer. For each 0 <= j <= n-1 we let C_n^j denote the Cayley graph of the cyclic group Zn with respect to the subset {1,j}. Utilizing the Smith Normal Form process, we give an explicit description of the Grothendieck group of each of the Leavitt path algebras LK(C_n^j) for any  field K. Our general method significantly streamlines the approach that was used in previous work to establish this description in the specific case j = 2. Along the way, we give necessary and sufficient conditions on the pairs (j; n) which yield that this group is infinite. We subsequently focus on the case j = 3, where the structure of this group turns out to be related to a Fibonacci-like sequence, called the Narayana's Cows sequence. 2024-02-21T13:20:50Z 2024-02-21T13:20:50Z 2024-02-21T13:20:50Z 2018-09-15 journal article Abrams, G., Erickson, S. & Gil Canto, C. Leavitt Path Algebras of Cayley Graphs . Mediterr. J. Math. 15, 197 (2018). https://doi.org/10.1007/s00009-018-1246-1 https://hdl.handle.net/10630/30584 10.1007/s00009-018-1246-1 eng open access Springer Nature