Toshitaka Aoki

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math.RT2025

Fans and polytopes in tilting theory III: Classification of convex $g$ -fans of rank 3

Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2

The $g$ -fan $I^£ (A)$ of a finite dimensional algebra $A$ is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union $P (A)$ of the simplices…

math.RT2025

Dimensions of $I ¨ $ -tilting modules over path algebras and preprojective algebras of Dynkin type

Toshitaka Aoki, Yuya Mizuno

In this paper, we introduce a new generating function called $d$ -polynomial for the dimensions of $I ¨ $ -tilting modules over a given finite dimensional algebra. Firstly, we study ba…

Fans and polytopes in tilting theory III: Classification of convex g-fans of rank 3

Dimensions of I¨-tilting modules over path algebras and preprojective algebras of Dynkin type

Fans and polytopes in tilting theory III: Classification of convex $g$ -fans of rank 3

Dimensions of $I ¨ $ -tilting modules over path algebras and preprojective algebras of Dynkin type