3 papers
math.RT2025
Tilting theoretic approach to quasi-hereditary structures
Takahide Adachi, Aaron Chan, Yuta Kimura +1
A quasi-hereditary algebra is an algebra equipped with a certain partial order on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives…
math.RT2025
Frobenius--Perron dimension via -tilting theory
Takahide Adachi, Ryoichi Kase
From the perspective of -tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of -tilti…
math.RT2024
On -tilting theory
Takahide Adachi, Osamu Iyama, Idun Reiten
We give a brief introduction to -tilting theory [AIR]. In particular, we will see how our theory unifies two different branches of tilting theory, namely, silting theory and cl…