Finite-dimensional algebras are (m>2)-Calabi-Yau-tilted
Sefi Ladkani
TL;DR
This paper demonstrates that over an algebraically closed field, every finite-dimensional algebra can be realized as an endomorphism algebra of an m-cluster-tilting object within an m-Calabi-Yau triangulated category for any m > 2.
Contribution
It establishes a universal construction linking finite-dimensional algebras to m-Calabi-Yau categories via m-cluster-tilting objects, extending known results to all m > 2.
Findings
Any finite-dimensional algebra is an endomorphism algebra of an m-cluster-tilting object
The construction works over algebraically closed fields
Applicable for all integers m > 2
Abstract
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons