
Dr Paul Truman
- Title
- Senior Lecturer
- Location
- MacKay Building Room 2.16
- Phone
- +44 (0) 1782 733246
- p.j.truman@keele.ac.uk
Biography
Biography
As an undergraduate, I read for an MMath at the University of Oxford (Exeter College). I graduated in 2005 and moved to the University of Exeter where I studied for a PhD in algebraic number theory under the supervision of Nigel Byott. After submitting my thesis I held two short term posts in Exeter, initially as a Research Fellow and subsequently as a Teaching Fellow. I came to Keele in 2010 as a Teaching Fellow; I was promoted to Lecturer (education and research) in 2013 and to Senior Lecturer in 2020.
Research and scholarship
Research and scholarship
My research interests are in algebra and number theory. Much of my work is connected with Hopf-Galois theory, a generalization of classical Galois theory which uses a Hopf algebra in place of the Galois group. I have studied the structure and properties of the Hopf algebras that occur in this context, and the applications of Hopf-Galois theory to questions of integral module structure in extensions of local or global fields.
I also study skew braces, which were introduced as tools to study set-theoretic solutions to the Yang-Baxter equation. There is a correspondence between skew braces and Hopf-Galois structures on Galois field extensions, and I am interested in how this correspondence can be used to translate structural results from one topic to the other. In a project funded by the EPSRC I introduced skew bracoids, a generalization of skew braces that correspond with Hopf-Galois structures on separable, but potentially non-normal, field extensions.
I was the corresponding author and chief copy editor for the research monograph Hopf algebras and Galois module theory, which was published by the American Mathematical Society in 2021, and I maintain an archive of the talks given at the annual conference Hopf algebras and Galois module theory.
I am interested in hearing from potential PhD students in Algebra and Algebraic Number Theory.
Teaching
Teaching
- MAT-30038 Number Theory and Cryptography
- MAT-30053 Guided Studies in Mathematics 1
- MAT-30055 Guided Studies in Mathematics 2
Publications
Publications
Journal Articles
- Truman, Paul; Martin-Lyons, Isabel. 15-01-2024. 'Skew Bracoids'. Journal of Algebra. DOI > view in repository >
- Truman. 01-02-2023. 'On ρ-conjugate Hopf–Galois structures'. Proceedings of the Edinburgh Mathematical Society. DOI > view in repository >
- Koch, Alan; Truman, Paul J.. 15-04-2022. 'Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions'. Journal of Algebra and Its Applications. DOI > view in repository >
- Koch, Alan; Stordy, Laura; Truman, Paul J.. 08-12-2020. 'Abelian fixed point free endomorphisms and the Yang-Baxter equation'. New York Journal of Mathematics. view in repository >
- Truman, Paul J.. 01-05-2020. 'Hopf-Galois module structure of tamely ramified radical extensions of prime degree'. Journal of Pure and Applied Algebra. DOI > view in repository >
- Koch, Alan; Truman, Paul. 15-03-2020. 'Opposite Skew Left Braces and Applications'. Journal of Algebra. DOI > view in repository >
- Koch, Alan; Kohl, Timothy; Truman, Paul J.; Underwood, Robert. 01-05-2019. 'Isomorphism problems for Hopf-Galois structures on separable field extensions'. Journal of Pure and Applied Algebra. DOI > view in repository >
- Truman, Paul; Taylor, Stuart. 05-03-2019. 'The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions'. New York Journal of Mathematics. view in repository >
- Koch, Alan; Kohl, Timothy; Truman, Paul J.; Underwood, Robert. 22-02-2019. 'Normality and Short Exact Sequences of Hopf-Galois Structures'. Communications in Algebra. DOI > view in repository >
- Truman. 01-06-2018. 'Commutative Hopf-Galois module structure of tame extensions'. Journal of Algebra. DOI > view in repository >
- Truman. 01-02-2018. 'Commuting Hopf-Galois structures on a separable extension'. Communications in Algebra. DOI > view in repository >
- Truman, Paul. 29-01-2016. 'Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions'. Communications in Algebra. DOI > view in repository >
- Truman. 01-01-2016. 'Hopf-Galois module structure of tame biquadratic extensions'. Journal de Theorie des Nombres de Bordeaux. DOI > view in repository >
- Truman, Paul. 01-01-2016. 'Hopf-Galois module structure of tame Cp×Cp extensions'. Journal de Theorie des Nombres de Bordeaux. DOI > view in repository >
- Truman, Paul. 09-10-2013. 'Integral Hopf-Galois structures for tame extensions'. New York Journal of Mathematics. view in repository >
- Truman. 17-12-2011. 'Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures'. New York Journal of Mathematics. view in repository >
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Book
- Childs, Lindsay; Greither, Cornelius; Keating, Kevin; Koch, Alan; Kohl, Timothy; Truman, Paul; Underwood, Robert. 01-01-2021. 'Hopf Algebras and Galois Module Theory'. . DOI > view in repository >
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Book Chapter
- Koch, Alan; Kohl, Timothy; Truman, Paul J.; Underwood, Robert. 27-02-2019. 'The Structure of Hopf Algebras Acting on Dihedral Extensions'. . view in repository >
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Research themes
Research themes
Pure Mathematics
School of Computer Science and Mathematics
Keele University
Staffordshire
ST5 5AA
Email: scm.admin@keele.ac.uk
Tel:+44 (0) 1782 731830