Degree-inverting involution on full square and triangular matrices
Lais S. da Fonseca, Ednei A. Santulo, Felipe Y. Yasumura
Abstract
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
Table of Contents
Fetching ...
Degree-inverting involution on full square and triangular matrices
Abstract
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
Paper Structure
This paper contains 10 sections, 23 theorems, 42 equations.
Table of Contents
- Introduction
- Preliminaries
- Graded Algebras
- Factor sets
- Graded division algebras
- Realization of graded division algebras with commutative support
- Degree-inverting involution on graded division algebras
- Abelian case
- Degree-inverting involution on matrix algebras
- Degree-inverting involution on upper triangular matrices
Key Result
Lemma 1
Let $\sigma_1,\sigma_2\in Z^2(T,\mathbb{F}^\times)$. Then $\mathbb{F}^{\sigma_1}T\cong\mathbb{F}^{\sigma_2}T$ if and only if $[\sigma_1]=[\sigma_2]$.∎
Theorems & Definitions (41)
- Definition
- Lemma 1: Kap1
- Lemma 2
- Lemma 3
- proof
- Proposition 4
- proof
- Lemma 5
- proof
- Lemma 6
- ...and 31 more