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- W3080600962 abstract "If A is an artin algebra, Gelinas has introduced an interesting upper bound for the finitistic dimension of A, namely the delooping level del A. We assert that for any Nakayama algebra, its finitistic dimension is equal to del A. This yields also a new proof that the finitistic dimension of A and of its opposite algebra are equal, as shown recently by Sen. If S is a simple module, let e(S) be the minimum of the projective dimension of S and of its injective envelope (one of these numbers has to be finite); and e*(S) the minimum of the injective dimension of S and of its projective cover. Then the finitistic dimension of A is 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 h of the simple modules S such that e*(h(S)) = e(S). In particular, this shows for any natural number z, that the number of simple modules S with e(S) = z is equal to the number of simple modules S' with e(S') = z." @default.
- W3080600962 created "2020-09-01" @default.
- W3080600962 creator A5070631310 @default.
- W3080600962 date "2020-08-23" @default.
- W3080600962 modified "2023-09-27" @default.
- W3080600962 title "The finitistic dimension of a Nakayama algebra" @default.
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