Decomposable quadratic forms and involutions
(2006) Journal of Algebra — Vol. 298, n° 2, p. 612-629 (2006)
Files
772006.pdf
Restricted Access - Adobe PDF
- 157.63 KB
pdfdocument.pdf
Restricted Access - Adobe PDF
- 157.63 KB
Details
- Authors
- Abstract
- In his book on compositions of quadratic forms, Shapiro asks whether a quadratic form decomposes as a tensor product of quadratic forms when its adjoint involution decomposes as a tensor product of involutions on central simple algebras. We give a positive answer for quadratic forms defined over local or global fields (or, more generally, over any linked field) and produce counterexamples over fields of rational fractions in two variables over any formally real field.
- Affiliations
Citations
Lewis, D. W., Mahmoudi, M. G., Tignol, J.-P., & Villa, O. (2006). Decomposable quadratic forms and involutions. Journal of Algebra, 298(2), 612-629. https://doi.org/10.1016/j.jalgebra.2005.10.030 (Original work published 2006)