A proof of the strong no loop conjecture.

DOI10.1016/j.aim.2011.06.042zbMath1237.16008arXiv1103.5361OpenAlexW2023854993WikidataQ122984232 ScholiaQ122984232MaRDI QIDQ645218

Shiping Liu, Charles Paquette, Kiyoshi Igusa

Publication date: 8 November 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5361

zbMATH Keywords

finite-dimensional algebrasprojective dimensionquiversHochschild homologysimple modulesArtin algebrasstrong no loop conjecture

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (15)

Spherical subcategories in representation theory ⋮ Hirzebruch-Riemann-Roch and Lefschetz type formulas for finite dimensional algebras ⋮ Vanishing of self-extensions over symmetric algebras. ⋮ Homological dimensions for co-rank one idempotent subalgebras ⋮ A method for constructing minimal projective resolutions over idempotent subrings ⋮ A characterization of hereditary algebras via thick subcategories ⋮ Injective representations of bound quiver algebras ⋮ HOMOLOGICAL DIMENSIONS OF CROSSED PRODUCTS ⋮ Notes on the Hochschild homology dimension and truncated cycles. ⋮ Cohomological comparison theorem ⋮ A bimodule approach to the strong no loop conjecture. ⋮ A New Characterization of Hereditary Algebras ⋮ Homological behavior of idempotent subalgebras and Ext algebras ⋮ Idempotent reduction for the finitistic dimension conjecture ⋮ Algebras of Finite Global Dimension

Cites Work

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• On the derived category of a finite-dimensional algebra
• The strong no loop conjecture for mild algebras.
• Artin rings of global dimension two
• Notes on the no loops conjecture
• On the cyclic homology of monomial relation algebras
• Left monomial rings -- a generalization of monomial algebras
• Extensions of abelian categories and the strong no-loops conjecture
• Cohomological reduction by split pairs.
• Nilpotente Elemente in Ringen von endlicher globaler Dimension
• Centerless groups -- an algebraic formulation of Gottlieb's theorem
• Minimal projective resolutions
• Strictly Stratified Algebras Revisited
• Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras
• Homological Aspects of Semigroup Gradings on Rings and Algebras
• Strong no-loop conjecture for algebras with two simples and radical cube zero
• The strong no loop conjecture for special biserial algebras
• Rank Element of a Projective Module

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