On genus of division algebras
| Autor: | Sergey V. Tikhonov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computer Science::Machine Learning
Degree (graph theory) General Mathematics 010102 general mathematics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Field (mathematics) Mathematics - Rings and Algebras Algebraic geometry 01 natural sciences Combinatorics Nonlinear Sciences::Exactly Solvable and Integrable Systems Number theory Rings and Algebras (math.RA) Genus (mathematics) 0103 physical sciences Condensed Matter::Statistical Mechanics FOS: Mathematics Exponent Division algebra 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | manuscripta mathematica. 164:321-325 |
| ISSN: | 1432-1785 0025-2611 |
| Popis: | The genus $gen(D)$ of a finite-dimensional central division algebra $D$ over a field $F$ is defined as the collection of classes $[D']\in Br(F)$, where $D'$ is a central division $F$-algebra having the same maximal subfields as $D$. We show that the fact that quaternion division algebras $D$ and $D'$ have the same maximal subfields does not imply that the matrix algebras $M_l(D)$ and $M_l(D')$ have the same maximal subfields for $l>1$. Moreover, for any odd $n>1$, we construct a field $L$ such that there are two quaternion division $L$-algebras $D$ and $D'$ and a central division $L$-algebra $C$ of degree and exponent $n$ such that $gen(D) = gen(D')$ but $gen(D \otimes C) \ne gen(D' \otimes C)$. This is a pre-print of an article published in manuscripta mathematica. The final authenticated version is available online at: https://doi.org/10.1007/s00229-020-01184-4 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink