Mai Katada

activity

20212026

most citedActions of automorphism groups of free groups on spaces of Jacobi diagrams. II

2 citations · 2 across the 6 of their papers we have counts for

collaborators

9 papers

math.RT2026

Quasi-cellular categories and the structure of the Brauer category

Kazuo Habiro, Mai Katada

We introduce the notion of a quasi-cellular category, which is a variant of cellular algebras and cellular categories. Many diagram categories, such as the Brauer category and the…

math.FA2026

A family of generalized Gelfand pairs attached to $3$ -step nilpotent Lie groups

Mai Katada, Cornelie Mitcha Malanda

It is well known that if $(K ⋉ N, K)$ is a Gelfand pair with $N$ a nilpotent Lie group and $K$ a compact subgroup of the automorphism group of $N$ , then $N$ is at most $2$ -ste…

math.AT2024

The stable Albanese homology of the IA-automorphism groups of free groups

Mai Katada

The IA-automorphism group $IA_{n}$ of the free group $F_{n}$ of rank $n$ is a normal subgroup of the automorphism group $Aut (F_{n})$ of $F_{n}$ . We study the…

math.AT2023

The first homology of $IA_{n}$ with coefficients in spaces of Jacobi diagrams

Mai Katada

The aim of this paper is to compute the first homology of $IA_{n}$ with coefficients in the $Aut (F_{n})$ -module $A_{2} (n)$ of Jacobi diagrams of degree $2$ …

math.AT2022

On Borel's stable range of the twisted cohomology of $GL (n, Z)$

Kazuo Habiro, Mai Katada

Borel's stability and vanishing theorem gives the stable cohomology of $GL (n, Z)$ with coefficients in algebraic $GL (n, Z)$ -representations. We co…

math.AT2022

On the stable cohomology of the IA-automorphism groups of free groups

Kazuo Habiro, Mai Katada

Borel's stability and vanishing theorem gives the stable cohomology of $GL (n, Z)$ with coefficients in algebraic $GL (n, Z)$ -representations. By co…

math.AT2022

Stable rational homology of the IA-automorphism groups of free groups

Mai Katada

The rational homology of the IA-automorphism group $IA_{n}$ of the free group $F_{n}$ is still mysterious. We study the quotient of the rational homology of $\operatorna…

math.GT2021★ 2 cited

Actions of automorphism groups of free groups on spaces of Jacobi diagrams. II

Mai Katada

The automorphism group $Aut (F_{n})$ of the free group $F_{n}$ acts on a space $A_{d} (n)$ of Jacobi diagrams of degree $d$ on $n$ oriented arcs. We study the $\operatorname…

math.QA2021

Actions of automorphism groups of free groups on spaces of Jacobi diagrams. I

Mai Katada

We consider an action of the automorphism group $Aut (F_{n})$ of the free group $F_{n}$ of rank $n$ on the filtered vector space $A_{d} (n)$ of Jacobi diagrams of degree $d$ on $n…

Quasi-cellular categories and the structure of the Brauer category

A family of generalized Gelfand pairs attached to 3-step nilpotent Lie groups

The stable Albanese homology of the IA-automorphism groups of free groups

The first homology of IAn​ with coefficients in spaces of Jacobi diagrams

On Borel's stable range of the twisted cohomology of GL(n,Z)

On the stable cohomology of the IA-automorphism groups of free groups

Stable rational homology of the IA-automorphism groups of free groups

Actions of automorphism groups of free groups on spaces of Jacobi diagrams. II

Actions of automorphism groups of free groups on spaces of Jacobi diagrams. I

A family of generalized Gelfand pairs attached to $3$ -step nilpotent Lie groups

The first homology of $IA_{n}$ with coefficients in spaces of Jacobi diagrams

On Borel's stable range of the twisted cohomology of $GL (n, Z)$