Hall algebras of extriangulated categories
Li Wang, Jiaqun Wei, Haicheng Zhang
TL;DR
This paper extends the concept of Hall algebras to extriangulated categories, unifying the algebraic structures associated with both exact and triangulated categories.
Contribution
It generalizes the definitions of Hall algebras from exact and triangulated categories to the broader framework of extriangulated categories.
Findings
Unified framework for Hall algebras in extriangulated categories
Extension of Hall algebra concepts to new categorical structures
Potential applications in representation theory and algebraic geometry
Abstract
Recently, Nakaoka and Palu introduced a notion of extriangulated categories. This is a unification of exact categories and triangulated categories. In this paper, we generalize the definitions of Hall algebras of exact categories and triangulated categories to extriangulated categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology