Yuya Mizuno

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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

Derived preprojective algebras and spherical twist functors

Yuya Mizuno, Dong Yang

We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Esp…

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…

math.RT2024

Shard theory for $g$ -fans

Yuya Mizuno

For a finite dimensional algebra $A$ , the notion of $g$ -fan $I^£ (A)$ is defined from two-term silting complexes of $A$ in the real Grothendieck group $K_0(\mathsf{proj} A)_{\mathbb{…

math.RT2024

$I ¨ $ -tilting theory and silting theory of skew group algebra extensions

Yuta Kimura, Ryotaro Koshio, Yuta Kozakai +2

Let $I^$ be a finite dimensional algebra with an action by a finite group $G$ and $A := I^ * G$ the skew group algebra. One of our main results asserts that the canonical restriction-…

math.RT2024

Fans and polytopes in tilting theory I: Foundations

Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2

For a finite dimensional algebra $A$ over a field $k$ , the 2-term silting complexes of $A$ gives a simplicial complex $I^ (A)$ called the $g$ -simplicial complex. We give tilting the…

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

Derived preprojective algebras and spherical twist functors

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

Shard theory for g-fans

I¨-tilting theory and silting theory of skew group algebra extensions

Fans and polytopes in tilting theory I: Foundations

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

Shard theory for $g$ -fans

$I ¨ $ -tilting theory and silting theory of skew group algebra extensions