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If A is a Nakayama algebra, we will show that fin-pro A = del A, thus, altogether fin-pro A = fin-inj A = del A = des A. The proof provides an explicit formula for the finitistic dimension of a Nakayama algebra A, namely fin pro A = max S min
Author: Claus Michael Ringel
Publish Year: 2021
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Theorem 2.6 Let Λ be an indecomposable Nakayama algebra with finite global dimension. Let ε : 0 → A → B → C → 0 be an almost split sequence and let n = pd A. Then the following are equivalent. (a) ε is an almost split sequence with inequality. (b) A ' Ω− (m−1) Ωm S or A ' Ω−m Ωm S, where S is a simple module with m = pd S an even number.
Author: Dag Madsen
Publish Year: 2005
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Given a connected (quiver) nonselfinjective Nakayama algebra with a circle as a quiver and at least two points. Such an algebra is determined by the (Kupisch) sequence [ c 0, c 1,..., c n − 1], when the algebra has n simples and c i is the dimension of the projective module at point i. We can furthermore always rotate and assume c n − 1 = c ...
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Primary Crusher. AC1410 / AC2415 / AC3219 / AC3219B / AC4219 / AC4220 / AC4220B / AC4820 / AC6030. Overview. Based on the design that focused on both asphalt and concrete crushing, AC crusher is the only available primary crusher in the market.
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We assert that for any Nakayama algebra A the finitistic dimension of A is equal to the delooping level. This yields also a new proof that the finitistic dimension of A and its opposite algebra are equal, as shown quite recently by Sen. View PDF on arXiv Save to Library Create Alert Delooping level of Nakayama algebras Emre Sen Mathematics 2020
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May 05, 2018 . Using our result on the bounds of global dimensions of Nakayama algebras, we give a short new proof of this result and generalise Brown’s result from quasi-hereditary to standardly stratified Nakayama algebras, where the global dimension is replaced with the finitistic dimension.
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Frobenius dimensions of Nakayama algebras 4 The Frobenius dimension F ( A) of an Artin algebra A is given by the dimension of H o m ( D ( A), A) (see the answer in On nearly Frobenius algebras ). Question 1: Is it true that F ( A) ≥ g l d i m ( A) for any Nakayama algebra A of finite global dimension?
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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.
Author: Claus Michael Ringel
Cite as: arXiv:2008.10044 [math.RT]
Publish Year: 2020
Subjects: Representation Theory (math.RT)
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Feb 15, 2018 . Let A be a non-selfinjective Nakayama algebra with n ≥ 3 simple modules. Then domdim ( A) ≤ 2 n − 3. In [1], Abrar calculated the dominant dimension for many Nakayama algebras and there the biggest value attained by a non-selfinjective Nakayama algebra with n simple modules was 2 n − 3, which lead him to his conjecture.
Author: René Marczinzik
Publish Year: 2018
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The finitistic dimension of a Nakayama algebra Ringel, Claus Michael If A is an artin algebra, Gélinas 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.
Author: Claus Michael Ringel
Publish Year: 2020
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Let A be an artin algebra, Gélinas has introduced an interesting upper bound for the finitistic dimension fin-pro A of A, namely the delooping level del A. We assert that fin-pro A = del A for any Nakayama algebra A. This yields also a new proof that the finitistic dimension of A and its opposite algebra are equal, as shown recently by Sen.
Such algebras contain many algebras over which the finitistic dimension conjecture holds, e.g., algebras of representation dimension at most 3, alge- bras with radical cube zero, monomial algebras and left serial algebras, etc. We provide many Igusa–Todorov algebras.
Let A be an artin algebra, Gélinas has introduced an interesting upper bound for the finitistic dimension fin-pro A of A, namely the delooping level del A. We assert that fin-pro A = del A for any Nakayama algebra A.
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).