Some examples of $t$-structures for finite-dimensional algebras

TL;DR

This paper explores the structure of $t$-structures in derived categories of finite-dimensional algebras, revealing new phenomena and characterizing the heart of the canonical $t$-structure via quadratic duals.

Contribution

It provides a new description of the heart of the canonical $t$-structure using quadratic duals, leading to novel examples of $t$-structure behavior.

Findings

Characterization of the heart as module category over quadratic dual

New phenomena in $t$-structures for finite-dimensional algebras

Examples illustrating these phenomena

Abstract

We describe the heart of the canonical $t$-structure on the perfect derived category of a strictly positive graded algebra as the module category over the quadratic dual. Applying this result we obtain examples showing new phenomena on $t$-structures on derived categories of finite-dimensional algebras.