Decomposable and Indecomposable Algebras of Degree 8 and Exponent 2
type: Dataset
description: We study the decomposition of central simple algebras of exponent $2$ into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let $B$ be a biquaternion algebra over $F(\sqrt{a})$ with trivial corestriction. A degree $3$ cohomological invariant is defined and we show that it determines whether $B$ has a descent to $F$. This invariant is used to give examples of indecomposable algebras of degree $8$ and exponent $2$ over a field of $2$-cohomological dimension $3$ and over a field $\mathbb M(t)$ where the $u$-invariant of $\mathbb M$ is $8$ and $t$ is an indeterminate. The construction of these indecomposable algebras uses Chow group computations provided by A. S. Merkurjev in Appendix.
issued: 2026-05-11T15:18:01.028959
language: en
modified: 2026-05-11T15:18:01.028963
contact point: Organization
  fn: CCSD
keyword: 11e81-16w10-12g10
keyword: central-simple-algebras
keyword: clifford-algebras
keyword: cohomological-dimension
keyword: galois-cohomology
keyword: infoeu-reposemanticspreprint
keyword: mathmath-ramathematics-mathrings-and-algebras-mathra
keyword: merkurjevs-theorem
keyword: preprints-working-papers-
keyword: quadratic-forms
landing page: https://hal.science/hal-00809490

Decomposable and Indecomposable Algebras of Degree 8 and Exponent 2
type: Distribution
format: HTML
issued: 2026-05-11T15:18:01.031057
modified: 2026-05-11T15:18:01.010293
access URL: https://hal.science/hal-00809490

test_moissonnage_selune
type: Agent