Thomas Unger

Preprint

(with Vincent Astier) Pfister's local-global principle for Azumaya algebras with involution. arXiv:2210.04851 (Updated 21 Oct 2024)

Publications

The life and work of David W. Lewis (1944-2021)
Irish Math. Soc. Bull. 82 (2022), 5-16
DOI: 10.33232/BIMS.0089.5.16
Positive cones and gauges on algebras with involution
    with Vincent Astier
    International Mathematics Research Notices, Volume 2022, Issue 10 (2022), 7259-7303
    DOI: 10.1093/imrn/rnaa337
    Preprint version: arXiv:1806.05489
Positive cones on algebras with involution
    with Vincent Astier
    Adv. Math. 361 (2020), 106954, 1-48
    DOI: 10.1016/j.aim.2019.106954
    Preprint version: arXiv:1609.06601
Galois extensions, positive involutions and an application to unitary space-time coding
    with Vincent Astier
    Adv. Math. Commun. 13 (3) (2019), 513-516
    DOI: 10.3934/amc.2019032
    Preprint version: arXiv:1809.08954
Positive cones and gauges on algebras with involution
    with Vincent Astier
    Oberwolfach Reports 15 (2) (2018), 1253-1255
    DOI: 10.4171/OWR/2018/21
    (preprint version)
Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
    with Vincent Astier
    J. Algebra 508 (2018), 339-363
    DOI: 10.1016/j.jalgebra.2018.05.004
    Preprint version: arXiv:1511.06330
Signatures, sums of hermitian squares and positive cones on algebras with involution
    with Vincent Astier
    Electron. Res. Announc. Math. Sci. 25 (2018), 16-26
    DOI: 10.3934/era.2018.25.003
    Preprint version: arXiv:1706.01264
Weakly hyperbolic involutions
    with Karim Johannes Becher
    Expo. Math. 36 (2018), 78-97
    DOI: 10.1016/j.exmath.2017.08.006
    Preprint version: arXiv:1207.4658
Stability index for algebras with involution
    with Vincent Astier
    Contemporary Mathematics 697 (2017), 41-50
    DOI: 10.1090/conm/697/14045
    Preprint version: arXiv:1406.5892
Algebraic structures for capturing the provenance of SPARQL queries
    with Floris Geerts, Grigoris Karvounarakis, Irini Fundulaki, Vassilis Christophides
    Journal of the ACM, Vol. 63, No. 1, Article 7 (2016), 7:1-7:63
    DOI: 10.1145/2810037
Signatures of hermitian forms and "prime ideals" of Witt groups
    with Vincent Astier
    Adv. Math. 285 (2015), 497-514
    DOI: 10.1016/j.aim.2015.07.035
    Preprint version: arXiv:1303.3494
Signatures of hermitian forms and the Knebusch Trace Formula
    with Vincent Astier
    Math. Annalen 358 (3-4) (2014), 925-947
    DOI: 10.1007/s00208-013-0977-3
    Preprint version (= final version plus erratum): arXiv:1003.0956
Signatures of hermitian forms and applications
    with Vincent Astier
    Oberwolfach Reports 10 (2) (2013), 1853-1856
    DOI: 10.4171/OWR/2013/31
    (preprint version)
Space-time block codes from nonassociative division algebras
    with Susanne Pumplün
    Adv. Math. Commun. 5 (3) (2011), 449-471
    DOI: 10.3934/amc.2011.5.449
    Preprint version: arXiv:1006.2348
Quadratic forms and space-time block codes from generalized quaternion and biquaternion algebras
    with Nadya Markin
    IEEE Trans. Inf. Theory 57 (9) (2011), 6148-6156
    DOI: 10.1109/TIT.2011.2161909
    Preprint version: arXiv:0807.0199
    [Annoying typo: in equation (4), x should be replaced by j.]
The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
    with Igor Klep
    J. Algebra 324 (2010), 256-268
    DOI: 10.1016/j.jalgebra.2010.03.022
    Preprint version: arXiv:0810.5254
The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
    with Igor Klep
    Oberwolfach Reports 6 (2) (2009), 1388-1390
    DOI: 10.4171/OWR/2009/25
    (preprint version)
A hermitian analogue of the Bröcker-Prestel theorem
    with Vincent Astier
    Indagationes Mathematicae (N.S.) 19 (3) (2008), 349-358
    DOI: 10.1016/S0019-3577(09)00007-X
Hermitian Morita Theory: a matrix approach
    with David W. Lewis
    Irish Math. Soc. Bull. 62 (2008), 37-41.
    Erratum (updated April 2018)
The Hasse principle for similarity of hermitian forms
    with David W. Lewis and Jan Van Geel
    J. Algebra 285 (2005), 196-212.
    DOI: 10.1016/j.jalgebra.2004.12.002
The hermitian level of composition algebras
    with Susanne Pumplün
    manuscripta mathematica 109 (2002), 511-525.
    DOI: 10.1007/s00229-002-0323-7
A local-global principle for algebras with involution and hermitian forms
    with David W. Lewis
    Math. Zeit. 244 (2003), 469-477.
    DOI: 10.1007/s00209-003-0490-6,
    Erratum
A weak Hasse principle for central simple algebras with an involution
    with David W. Lewis and Claus Scheiderer
    Doc. Math. Extra Volume, Proc. Conf. Quadratic Forms and Related Topics, Baton
    Rouge, La., 2001, 241-251 (2001)
A note on surrogate forms of central simple algebras
Math. Proc. R. Ir. Acad., 101A(2) (2001), 125-135.
Clifford algebra periodicity for central simple algebras with an involution
Comm. Algebra, 29(3) (2001), 1141-1152.
DOI: 10.1081/AGB-100001672
Genetic Algorithms: a survey of some mathematical models --- Part I
Irish Math. Soc. Bull. 41 (1998), 57-71.

Not Peer Reviewed

Signatures, sums of hermitian squares and positive cones on algebras with involution
with Vincent Astier
Séminaire de Structures Algébriques Ordonnées 2015-2016, 91 (2017)
Signatures of hermitian forms, prime ideals and morphisms
with Vincent Astier
Séminaire de Structures Algébriques Ordonnées 2012-2013, 89 (2014)

Books

Real Algebra: A First Course by Manfred Knebusch and Claus Scheiderer
Translated and with contributions by Thomas Unger

Universitext, Springer Nature, 2022
DOI: 10.1007/978-3-031-09800-0
(Revised and updated English translation of Einführung in die reelle Algebra.)
Specialization of Quadratic and Symmetric Bilinear Forms by Manfred Knebusch
Translated by Thomas Unger

Algebra and Applications, Vol. 11, Springer, 2010
DOI: 10.1007/978-1-84882-242-9
The original German version Spezialisierung von quadratischen und symmetrisch bilinearen Formen can be downloaded here: (link).

Last updated: 22 November 2024