Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T03:37:55.289Z Has data issue: false hasContentIssue false
  • English
  • Français

SYMMETRIC SQUARE-CENTRAL ELEMENTS IN PRODUCTS OF ORTHOGONAL INVOLUTIONS IN CHARACTERISTIC TWO

Part of: Division rings and semisimple Artin rings Forms and linear algebraic groups Rings and algebras with additional structure

Published online by Cambridge University Press:  17 August 2017

A.-H. NOKHODKAR
A.-H. NOKHODKAR*
Affiliation:
Department of Pure Mathematics, Faculty of Science, University of Kashan, PO Box 87317-51167, Kashan, Iran email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In characteristic two, some criteria are obtained for a symmetric square-central element of a totally decomposable algebra with orthogonal involution, to be contained in an invariant quaternion subalgebra.

Keywords

central simple algebratotally decomposable algebrasquare-central elementorthogonal involutionquaternion subalgebra

MSC classification

Primary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures
Secondary: 16K20: Finite-dimensional 11E39: Bilinear and Hermitian forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 412 - 425
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Arason, J. and Baeza, R., ‘Relations in I n and I n W q in characteristic 2’, J. Algebra 314(2) (2007), 895–911.CrossRefGoogle Scholar
Barry, D., ‘Decomposable and indecomposable algebras of degree 8 and exponent 2 (with an appendix by A. S. Merkurjev)’, Math. Z. 276(3–4) (2014), 1113–1132.CrossRefGoogle Scholar
Barry, D., ‘Power-central elements in tensor products of symbol algebras’, Comm. Algebra 44(9) (2016), 3767–3787.CrossRefGoogle Scholar
Barry, D. and Chapman, A., ‘Square-central and Artin–Schreier elements in division algebras’, Arch. Math. (Basel) 104(6) (2015), 513–521.CrossRefGoogle Scholar
Dolphin, A., ‘Orthogonal Pfister involutions in characteristic two’, J. Pure Appl. Algebra 218(10) (2014), 1900–1915.CrossRefGoogle Scholar
Elman, R., Karpenko, N. and Merkurjev, A., The Algebraic and Geometric Theory of Quadratic Forms, American Mathematical Society Colloquium Publications, 56 (American Mathematical Society, Providence, RI, 2008).CrossRefGoogle Scholar
Hoffmann, D., ‘Witt kernels of bilinear forms for algebraic extensions in characteristic 2’, Proc. Amer. Math. Soc. 134(3) (2006), 645–652.CrossRefGoogle Scholar
Jacobson, N., Finite-dimensional Division Algebras Over Fields (Springer, Berlin, 1996).CrossRefGoogle Scholar
Knus, M.-A., Merkurjev, A. S., Rost, M. and Tignol, J.-P., The Book of Involutions, American Mathematical Society Colloquium Publications, 44 (American Mathematical Society, Providence, RI, 1998).CrossRefGoogle Scholar
Knus, M.-A., Parimala, R. and Sridharan, R., ‘Involutions on rank 16 central simple algebras’, J. Indian Math. Soc. (N.S.) 57(1–4) (1991), 143–151.Google Scholar
Mahmoudi, M. G. and Nokhodkar, A.-H., ‘On split products of quaternion algebras with involution in characteristic two’, J. Pure Appl. Algebra 218(4) (2014), 731–734.CrossRefGoogle Scholar
Mahmoudi, M. G. and Nokhodkar, A.-H., ‘On totally decomposable algebras with involution in characteristic two’, J. Algebra 451 (2016), 208–231.CrossRefGoogle Scholar
Nokhodkar, A.-H., ‘Quadratic descent of totally decomposable orthogonal involutions in characteristic two’, J. Pure Appl. Algebra 221(4) (2017), 948–959.CrossRefGoogle Scholar
Nokhodkar, A.-H., ‘On the decomposition of metabolic involutions’, J. Algebra Appl. , doi:10.1142/S0219498817501298.Google Scholar
Nokhodkar, A.-H., ‘On decomposable biquaternion algebras with involution of orthogonal type’, 2016, arXiv:1508.02018.Google Scholar
Nokhodkar, A.-H., ‘Orthogonal involutions and totally singular quadratic forms in characteristic two’, Manuscripta Math. (2017), doi:10.1007/s00229-017-0922-y.Google Scholar
Quéguiner-Mathieu, A. and Tignol, J.-P., ‘Discriminant and Clifford algebras’, Math. Z. 240(2) (2002), 345–384.CrossRefGoogle Scholar
Rowen, L. H., ‘Central simple algebras’, Israel J. Math. 29 (1978), 285–301.CrossRefGoogle Scholar