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Igusa-Todorov ϕ Function for Truncated Path Algebras

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Abstract

Given a truncated path algebra \(A=\frac {\Bbbk Q}{J^{k}}\) we prove that ϕ dimA = ϕ dimAop. We also compute the ϕ-dimension of A as a function of the ϕ-dimension of \(\frac {\Bbbk Q}{J^{2}}\) when Q has no sources nor sinks. This allows us to bound the ϕ-dimension for truncated path algebras. Finally, we characterize A when its ϕ-dimension is equal to 1.

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Authors and Affiliations

  1. Universidad de la República, Montevideo, Uruguay

    Marcos Barrios, Gustavo Mata & Gustavo Rama

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  1. Marcos Barrios
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  2. Gustavo Mata
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  3. Gustavo Rama
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Correspondence to Gustavo Mata.

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Presented by: Henning Krause

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Barrios, M., Mata, G. & Rama, G. Igusa-Todorov ϕ Function for Truncated Path Algebras. Algebr Represent Theor 23, 1051–1063 (2020). https://doi.org/10.1007/s10468-019-09883-7

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  • DOI: https://doi.org/10.1007/s10468-019-09883-7

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