Superpotentials and higher order derivations.

DOI10.1016/j.jpaa.2009.07.013zbMath1219.16016arXiv0802.0162OpenAlexW2015907220MaRDI QIDQ964507

Michael Wemyss, Raf Bocklandt, Travis Schedler

Publication date: 22 April 2010

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0162

zbMATH Keywords

quiversderivationspath algebrasMcKay correspondencesuperpotentials

Mathematics Subject Classification ID

Representations of quivers and partially ordered sets (16G20) Graded rings and modules (associative rings and algebras) (16W50) Quadratic and Koszul algebras (16S37)

Related Items (60)

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Uses Software

• GAP

Cites Work

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• Irreducible representations of the \(4\)-dimensional Sklyanin algebra at points of infinite order
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras.
• Noncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheres
• Quivers with potentials and their representations. I: Mutations.
• Graded algebras of global dimension 3
• The four-dimensional Sklyanin algebras
• Noncommutative finite-dimensional manifolds. I: Spherical manifolds and related examples
• On quantum symmetries of ADE graphs
• Homogeneous algebras.
• Noncommutative deformations of Kleinian singularities
• Graded Calabi Yau algebras of dimension 3.
• Moduli of McKay quiver representations. II: Gröbner basis techniques
• Multilinear forms and graded algebras
• Koszul and Gorenstein properties for homogeneous algebras.
• Graded algebras and multilinear forms.
• Two-dimensional tame and maximal orders of finite representation type
• Regularity of Algebras Related to the Sklyanin Algebra
• Monodromy for systems of vector bundles and multiplicative preprojective algebras
• Koszulity for nonquadratic algebras.

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