Igusa-Todorov ϕ Function for Truncated Path Algebras

Given a truncated path algebra A = 𝕜Q J k we prove that ϕ dim A = ϕ dim A op . We also compute the ϕ -dimension of A as a function of the ϕ -dimension of 𝕜Q 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...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 23; no. 3; pp. 1051 - 1063
Main Authors Barrios, Marcos, Mata, Gustavo, Rama, Gustavo
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects
Algebra
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
Igusa-Todorov function
Truncated path algebra
Radical square zero algebra
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Summary:Given a truncated path algebra A = 𝕜Q J k we prove that ϕ dim A = ϕ dim A op . We also compute the ϕ -dimension of A as a function of the ϕ -dimension of 𝕜Q 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.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-019-09883-7