Split-By-Nilpotent Extensions Algebras and Stratifying Systems

Lanzilotta, Marcelo; Mendoza, Octavio; Sáenz, Corina

doi:10.1080/00927872.2013.830729

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…In that paper, they showed that one can associate to every stratifying system an object whose endomorphism algebra is standardly stratified. Since the stratified systems appeared in light, they have gotten a great amount of attention, see for instance [18,16,21,22,23,26,25,24,27,28,29,31,30,33].…”

Section: Introductionmentioning

confidence: 99%

Stratifying systems through $τ$-tilting theory

Mendoza¹,

Treffinger²

2019

Preprint

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In this paper we study the stratifying systems, introduced by K. Erdmann and C. Saenz in [17], by using the τ -tilting theory introduced by T. Adachi, O. Iyama and I. Reiten in [1]. We give a constructive proof that every non-zero τ -rigid module induces at least one stratifying system for any finite dimensional algebra A. Later, we show that each stratifying system found this way is a τ -exceptional sequence as defined by A. B. Buan and R. Marsh in [5].

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Section: Introductionmentioning

confidence: 99%

Stratifying systems through $τ$-tilting theory

Mendoza¹,

Treffinger²

2019

Preprint

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“…A special interesting type of cleft extensions are the split-by-nilpotent extension algebras (see [2], [16] and [17]).…”

Section: Introductionmentioning

confidence: 99%

Cyclic homology of cleft extensions of algebras

Guccione

Valqui

2018

J. Algebra Appl.

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Abstract. Let k be a commutative algebra with Q ⊆ k and let (E, p, i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E relative to ker(p). This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra.

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“…For instance the finitistic dimension of one is finite if and only if the finitistic dimension of the other is finite. A similar concept was defined and studied in [18].…”

Section: Introductionmentioning

confidence: 99%

Convex subquivers and the finitistic dimension

Green¹,

Marcos²

2017

Illinois J. Math.

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Let Q be a quiver and K a field. We study the interrelationship of homological properties of algebras associated to convex subquivers of Q and quotients of the path algebra KQ. We introduce the homological heart of Q which is a particularly nice convex subquiver of Q. For any algebra of the form KQ/I, the algebra associated to KQ/I and the homological heart have similar homological properties. We give an application showing that the finitistic dimension conjecture need only be proved for algebras with path connected quivers.

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Split-By-Nilpotent Extensions Algebras and Stratifying Systems

Abstract: Let Γ and Λ be artin algebras such that Γ is a split-bynilpotent extension of Λ by a two sided ideal I of Γ. Consider the socalled change of rings functors G := Γ

Cited by 4 publications

References 33 publications

Stratifying systems through $τ$-tilting theory

Stratifying systems through $τ$-tilting theory

Cyclic homology of cleft extensions of algebras

Convex subquivers and the finitistic dimension

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