Web page of Tom De Medts

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Tom De Medts @ Ghent University

Publications

Research articles

  1. Tom De Medts, Jeroen Meulewaeter
    5x5-graded Lie algebras, cubic norm structures and quadrangular algebras,
    in preparation.
  1. Tom De Medts, William Hautekiet
    Totally disconnected locally compact groups arising from transcendental field extensions,
    in preparation.
  1. Pierre-Emmanuel Caprace, Tom De Medts
    Lattice envelopes of right-angled Artin groups,
    33 pp, submitted.
Preprint
  1. Sigiswald Barbier, Tom De Medts, Michiel Smet
    Operator Kantor pairs,
    65 pp, submitted.
Preprint
  1. Tom De Medts, Louis Rowen, Yoav Segev
    Primitive 4-generated axial algebras of Jordan type,
    Proc. Amer. Math. Soc. 152 (2024), no. 2, 537–551.
DOI linkPreprint
  1. Tom De Medts, Mathias Stout
    Matsuo algebras in characteristic 2,
    J. Algebra (2024), 19 pp, to appear (available online).
DOI linkPreprint
  1. Jens Bossaert, Tom De Medts
    Restricted universal groups for right-angled buildings,
    Innov. Incidence Geom. 20 (2023), 177–208.
DOI linkPreprint
  1. Tom De Medts, Jeroen Meulewaeter
    Inner ideals and structurable algebras: Moufang sets, triangles and hexagons,
    Israel J. Math. (2023), 56 pp, to appear (available online).

    Read-only version on Springer SharedIt: http://rdcu.be/dfYle.

DOI linkPreprint
  1. Jens Bossaert, Tom De Medts
    City products of right-angled buildings and their universal groups,
    J. Algebra (2022), 25 pp, to appear (available online).
DOI linkPreprint
  1. Tom De Medts, Michiel Van Couwenberghe
    Non-associative Frobenius algebras for simply laced Chevalley groups,
    Trans. Amer. Math. Soc. 374 (2021), 8715–8774.
DOI linkPreprint
  1. Jens Bossaert, Tom De Medts
    Topological and algebraic properties of universal groups for right-angled buildings,
    Forum Math. 33 (2021), no. 4, 867–888.
DOI linkPreprint
  1. Tom De Medts, Simon Peacock, Sergey Shpectorov, Michiel Van Couwenberghe
    Decomposition algebras and axial algebras,
    J. Algebra 556 (2020), 287–314.
DOI linkPreprint
  1. Tom De Medts, Michiel Van Couwenberghe
    Modules over axial algebras,
    Algebr. Represent. Theory 23 (2020), no. 1, 209–227.

    Read-only version on Springer SharedIt: http://rdcu.be/bdZ2T.

DOI linkPreprint
  1. Tom De Medts, Bernhard Mühlherr, Anastasia Stavrova
    Mini-Workshop - Rank One Groups and Exceptional Algebraic Groups (52/2019),
    Oberwolfach Rep. 16 (2019), no. 4, 3243–3269.
DOI link
  1. Tom De Medts, Ana C. Silva
    Open subgroups of the automorphism group of a right-angled building,
    Geom. Dedicata 203 (2019), no. 1, 1–23.

    Read-only version on Springer SharedIt: http://rdcu.be/bgUEI.

DOI linkPreprint
  1. Tom De Medts
    Structurable algebras of skew-dimension one and hermitian cubic norm structures,
    Comm. Algebra 47 (2019), 154–172.
DOI linkPreprint
  1. Lien Boelaert, Tom De Medts, Anastasia Stavrova
    Moufang sets and structurable division algebras,
    Mem. Amer. Math. Soc. 259 (2019), no. 1245, 90 pp.

    Available from the AMS Bookstore.

Preprint
  1. Tom De Medts, Karsten Naert
    Suzuki-Ree groups as algebraic groups over F√p,
    16 pp, submitted.
Preprint
  1. Tom De Medts, Ana C. Silva, Koen Struyve
    Universal groups for right-angled buildings,
    Groups Geom. Dyn. 12 (2018), 231–287.
DOI linkPreprint
  1. Tom De Medts, Erik Rijcken
    Local Moufang sets and local Jordan pairs,
    J. Algebra 488 (2017), 66–109.
DOI linkPreprint
  1. Tom De Medts, Felix Rehren
    Jordan algebras and 3-transposition groups,
    J. Algebra 478 (2017), 318–340.

    Erratum: There is a computational error in the proof of the final theorem, on page 339, where the constant 1/32 should be 3/32. Surprisingly, this gives rise to a new infinite family of examples over fields of characteristic 3. This was discovered by Takahiro Yabe; see https://doi.org/10.1016/j.jalgebra.2018.07.018.

DOI linkPreprint
  1. Tom De Medts, Yoav Segev, Richard Weiss
    Tits endomorphisms and buildings of type F4,
    Ann. Inst. Fourier (Grenoble) 67 (2017), 2349–2421.
DOI linkPreprint
  1. Tom De Medts, Erik Rijcken
    Local Moufang sets and PSL2 over local rings,
    J. Group Theory 19 (2016), 815–847.
DOI linkPreprint
  1. Elizabeth Callens, Tom De Medts
    Moufang sets of mixed type F4,
    Math. Nachr. 288 (2015), no. 4, 366–388.
DOI linkPreprint
  1. Lien Boelaert, Tom De Medts
    A new construction of Moufang quadrangles of type E6, E7 and E8,
    Trans. Amer. Math. Soc. 367 (2015), 3447–3480.
DOI linkPreprint
  1. Elizabeth Callens, Tom De Medts
    Moufang sets arising from polarities of Moufang planes over octonion division algebras,
    Manuscripta Math. 143 (2014), 171–189.

    Read-only version on Springer SharedIt: http://rdcu.be/m1nt.

DOI linkPreprint
  1. Lien Boelaert, Tom De Medts
    Exceptional Moufang quadrangles and structurable algebras,
    Proc. London Math. Soc. 107 (2013), no. 3, 590–626.
DOI linkPreprint
  1. Pierre-Emmanuel Caprace, Tom De Medts
    Trees, contraction groups, and Moufang sets,
    Duke Math. J. 162 (2013), no. 13, 2413–2449.
DOI linkPreprint
  1. Tom De Medts, Attila Maróti
    Perfect numbers and finite groups,
    Rend. Semin. Mat. Univ. Padova 129 (2013), 17–33.

    See also the corresponding webpage.

DOI linkPreprint
  1. Pierre-Emmanuel Caprace, Tom De Medts
    Simple locally compact groups acting on trees and their germs of automorphisms,
    Transform. Groups 16 (2011), no. 2, 375–411.

    Read-only version on Springer SharedIt: http://rdcu.be/m1nq.

DOI linkPreprint
  1. Tom De Medts, Marius Tărnăuceanu
    Pseudocomplementation in (normal) subgroup lattices,
    Comm. Algebra 39 (2011), no. 1, 247–262.

    Erratum: As was pointed out by Roland Schmidt, there is a mistake in the last result of the paper (Theorem 5.12), where we incorrectly claimed that a group for which every subgroup is monolithic has cyclic Sylow subgroups. This is incorrect; they can have non-cyclic Sylow 2-subgroups.

DOI linkPreprint
  1. Tom De Medts, Richard Weiss
    The norm of a Ree group,
    Nagoya Math. J. 199 (2010), 15–41.
DOI linkPreprint
  1. Tom De Medts, Hendrik Van Maldeghem
    Moufang sets of type F4,
    Math. Z. 265 (2010), 511–527.

    Read-only version on Springer SharedIt: http://rdcu.be/m1nl.

DOI link
  1. Tom De Medts, Ralf Gramlich, Max Horn
    Iwasawa decompositions of split Kac-Moody groups,
    J. Lie Theory 19 (2009), no. 2, 311–337.

    Webpage: http://www.heldermann.de/JLT/JLT19/JLT192/jlt19017.htm

Preprint
  1. Tom De Medts, Yoav Segev
    A course on Moufang sets,
    Innov. Incidence Geom. 9 (2009), 79–122.
DOI link
  1. Tom De Medts, Hendrik Van Maldeghem
    The uniqueness of a generalized hexagon of order 3 containing a subhexagon of order (1,3),
    Discrete Math. 309 (2009), no. 4, 714–720.
DOI link
  1. Tom De Medts, Katrin Tent
    Central extensions of rank 2 groups and applications,
    Forum Math. 21 (2009), no. 1, 1–21.
DOI link
  1. Tom De Medts, Marius Tărnăuceanu
    Finite groups determined by an inequality of the orders of their subgroups,
    Bull. Belg. Math. Soc. Simon Stevin 15 (2008), 699–704.

    Open access: http://projecteuclid.org/euclid.bbms/1225893949

DOI link
  1. Tom De Medts, Katrin Tent
    Special abelian Moufang sets of finite Morley rank,
    J. Group Theory 11 (2008), no. 5, 645–655.
DOI link
  1. Tom De Medts, Yoav Segev
    Finite special Moufang sets of even characteristic,
    Commun. Contemp. Math. 10 (2008), no. 3, 449–454.

    See also the companion paper "Finite special Moufang sets of odd characteristic" by Y. Segev,
    Commun. Contemp. Math. 10 (2008), no. 3, 455–475.

DOI linkPreprint
  1. Tom De Medts, Yoav Segev, Katrin Tent
    Special Moufang sets, their root groups, and their μ-maps,
    Proc. London Math. Soc. 96 (2008), no. 3, 767–791.
DOI link
  1. Tom De Medts, Yoav Segev
    Identities in Moufang sets,
    Trans. Amer. Math. Soc. 360 (2008), 5831–5852.
DOI link
  1. Tom De Medts, Richard Weiss
    Moufang sets and Jordan division algebras,
    Math. Ann. 335 (2006), no. 2, 415–433.

    Read-only version on Springer SharedIt: http://rdcu.be/m1nj.

DOI link
  1. Tom De Medts
    Inclusions of irreducible spherical buildings of equal rank ≥ 3,
    Bull. Belg. Math. Soc. Simon Stevin 12 (2006), no. 5, 751–765.

    Open access: http://projecteuclid.org/euclid.bbms/1136902613

DOI link
  1. Tom De Medts
    A link between Moufang sets and Jordan division algebras,
    Oberwolfach Rep. 2 (2005), no. 1, 666–668.
DOI link
  1. Tom De Medts
    Algebraic inclusions of Moufang polygons,
    Forum Math. 17 (2005), no. 6, 921–957.
DOI link
  1. Tom De Medts, Fabienne Haot, Katrin Tent, Hendrik Van Maldeghem
    Split BN-pairs of rank at least 2 and the uniqueness of splittings,
    J. Group Theory 8 (2005), no. 1, 1–10.
DOI link
  1. Tom De Medts
    An algebraic structure for Moufang quadrangles,
    Mem. Amer. Math. Soc. 173 (2005), no. 818, 99 pp.

    Available from the AMS Bookstore.

  1. Tom De Medts
    Automorphisms of F4 quadrangles,
    Math. Ann. 328 (2004), 399–413.

    Read-only version on Springer SharedIt: http://rdcu.be/m1ng.

DOI link
  1. Tom De Medts
    A characterization of quadratic forms of type E6, E7 and E8,
    J. Algebra 252 (2002), 394–410.
DOI link

Book chapters

  1. Tom De Medts, Fabienne Haot, Rafael Knop, Hendrik Van Maldeghem
    "On the uniqueness of the unipotent subgroups of some Moufang sets",
    in: Finite Geometries, Groups, and Computation, Proceedings of the conference "Finite Geometries, Groups and Computation", September 4-9, 2004, Pingree Park, Colorado, USA (ed. A. Hulpke, R. Liebler, T. Penttila, A. Seress), (2006), 43–66.
    Walter de Gruyter, Berlin, New York.
Preprint
  1. Tom De Medts, Hendrik Van Maldeghem
    "Moufang generalized polygons",
    in: Topics in Diagram Geometry, Quaderni di Matematica 12 (2004), 59–126.
    Dipartimento di Matematica, Seconda Università degli Studi di Napoli.

    Webpage: http://www.dimat.unina2.it/quaderni/quaderni12.htm

Course notes

  1. Jan De Beule, Tom De Medts, Jeroen Demeyer
    Opgeloste en onopgeloste mysteries in de getaltheorie (2013),  38 pp.

    ISBN 9789048616633 — die Keure Printing and Publishing

  1. Tom De Medts
    Course notes "Linear Algebraic Groups", 10th version (2022-2023),  145 pp.
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Unpublished notes (not intended for publication)

  1. Tom De Medts
    Known examples of Moufang sets (2020),  24 pp.
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  1. Tom De Medts
    The isomorphism problem for Moufang sets of type 1D4(2) and the Bartels invariant (2017),  21 pp.
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  1. Tom De Medts
    The category of Moufang sets (2007),  4 pp.
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  1. Tom De Medts
    Non-abelian Moufang sets of type 2A3, C3 and F4 (2007),  3 pp.
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  1. Tom De Medts
    Moufang sets arising from Moufang polygons of type E6 and E7 (2006),  4 pp.
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