Derived invariants of gentle orders
Wassilij Gnedin
TL;DR
This paper investigates the derived representation theory of gentle orders, focusing on their invariants, Nakayama functor, and Calabi-Yau properties, extending known results from finite-dimensional gentle algebras to infinite-dimensional cases.
Contribution
It introduces new derived invariants for gentle orders and analyzes their Nakayama functor and Calabi-Yau properties, expanding the understanding of infinite-dimensional gentle algebras.
Findings
Derived invariants of the underlying quiver are established
Factorization of the derived Nakayama functor is provided
Fractionally Calabi-Yau objects and exceptional cycles are studied
Abstract
This article is concerned with the derived representation theory of certain infinite-dimensional gentle algebras called gentle orders. For a gentle order, we provide a factorization of the derived Nakayama functor, study its fractionally Calabi-Yau objects and exceptional cycles, and establish that certain combinatorial invariants of its underlying quiver are derived invariants, analogous to results for finite-dimensional gentle algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic