The finitistic dimension of a Nakayama algebra

Ringel CM (2021)
Journal of Algebra 576: 95-145.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let Abe an artin algebra, Gelinas has introduced an interesting upper bound for the finitistic dimension fin-pro A of A, namely the delooping level delA. We assert that fin-pro A = del A for any Nakayama algebra A. This yields also a new proof that the finitistic dimension of Aand its opposite algebra are equal, as shown recently by Sen. If Sis a simple module, let e(S) be the minimum of the projective dimension of Sand of its injective envelope (one of these numbers has to be finite); and e*(S) the minimum of the injective dimension of Sand of its projective cover. Then the finitistic dimension of Ais the maximum of the numbers e(S), as well as the maximum of the numbers e*(S). Using suitable syzygy modules, we construct a permutation hof the simple modules Ssuch that e*(h(S)) = e(S). In particular, this shows for z is an element of N that the number of simple modules S with e(S) = z is equal to the number of simple modules S' with e*(S') = z. (C) 2021 Elsevier Inc. All rights reserved.
Stichworte
Nakayama algebra; Finitistic dimension; Delooping level; Desuspending; level; The grade of a module; The homological permutation; Catalan; combinatorics
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Algebra
Band
576
Seite(n)
95-145
ISSN
0021-8693
eISSN
1090-266X
Page URI
https://pub.uni-bielefeld.de/record/2953391

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Ringel CM. The finitistic dimension of a Nakayama algebra. Journal of Algebra. 2021;576:95-145.
Ringel, C. M. (2021). The finitistic dimension of a Nakayama algebra. Journal of Algebra, 576, 95-145. https://doi.org/10.1016/j.jalgebra.2021.01.040
Ringel, C. M. (2021). The finitistic dimension of a Nakayama algebra. Journal of Algebra 576, 95-145.
Ringel, C.M., 2021. The finitistic dimension of a Nakayama algebra. Journal of Algebra, 576, p 95-145.
C.M. Ringel, “The finitistic dimension of a Nakayama algebra”, Journal of Algebra, vol. 576, 2021, pp. 95-145.
Ringel, C.M.: The finitistic dimension of a Nakayama algebra. Journal of Algebra. 576, 95-145 (2021).
Ringel, Claus Michael. “The finitistic dimension of a Nakayama algebra”. Journal of Algebra 576 (2021): 95-145.

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