Definable groups and compact p-adic Lie groups

Onshuus, A.; Pillay, A.
August 2008
Journal of the London Mathematical Society;Aug2008, Vol. 78 Issue 1, p233
Academic Journal
We formulate p-adic analogues of the o-minimal group conjectures from the works of Hrushovski, Peterzil and Pillay [J. Amer. Math. Soc., to appear] and Pillay [J. Math. Log. 4 (2004) 147–162]; that is, we formulate versions that are appropriate for groups G definable in (saturated) P-minimal fields. We then restrict our attention to saturated models K of Th(ℚp) and Th(ℚp, an), record some elementary observations when G is defined over the standard model ℚp, and then make a detailed analysis of the case where G = E(K) for E an elliptic curve over K. Essentially, our P-minimal conjectures hold in these contexts and, moreover, our case study of elliptic curves yields counterexamples to a more naive direct translation of the o-minimal conjectures.


Related Articles

  • Lie algebras of a class of top spaces. Molaei, M. R.; Farhangdoost, M. R. // Balkan Journal of Geometry & Its Applications;2009, Vol. 14 Issue 1, p46 

    In this paper 1-dimensional and 2-dimensional top spaces with finite numbers of identities and connected Lie group components are characterized. MF-semigroups are determined. By using of the left-invariant vector fields of top spaces and their one-parameter subgroups, a relation between the Lie...

  • Restriction of Representations of G2 to A2. Saenkarun, S.; Loutsiouk, A.; Chunrungsikul, S. // Southeast Asian Bulletin of Mathematics;2011, Vol. 35 Issue 4, p675 

    In this paper, we realized all finite-dimensional irreducible representations of the Lie group of class G2 in spaces of complex-valued polynomials of six variables. This realization is applied to the problem of restriction of representations of a Lie group of class G2 to a Lie subgroup of class A2.

  • Integration of Lie 2-Algebras and Their Morphisms. Sheng, Yunhe; Zhu, Chenchang // Letters in Mathematical Physics;Nov2012, Vol. 102 Issue 2, p223 

    Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the integration procedure of Getzler and Henriques will also produce a 2-group. In this paper, we show that these two integration results are...

  • On definability of addition in Lie algebras. Ponomarev, K. // Siberian Mathematical Journal;Nov2011, Vol. 52 Issue 6, p1065 

    An answer is obtained to I. V. Arzhantsev's question on definability of the structure of a semisimple Lie algebra by the multiplicative groupoid of L.

  • Inductive McKay condition in defining characteristic. Späth, Britta // Bulletin of the London Mathematical Society;Jun2012, Vol. 44 Issue 3, p426 

    We reformulate the inductive McKay condition, from Isaacs–Malle–Navarro, and apply the new criterion to simple groups of Lie type, when the prime is the defining characteristic p. Using a recent result of Maslowski, we obtain that these simple groups satisfy the inductive McKay...

  • Test rank of an abelian product of a free Lie algebra and a free abelian Lie algebra. EKICI, NAIME; ÖĞÜŞLÜ, NAZAR // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Aug2011, Vol. 121 Issue 3, p291 

    Let F be a free Lie algebra of rank n ≥ 2 and A be a free abelian Lie algebra of rank m ≥ 2. We prove that the test rank of the abelian product F × A is m. Morever we compute the test rank of the algebra $F/\gamma _{k}\left( F\right) ^{^{\prime }}$.

  • A zoo of diffeomorphism groups on $$\mathbb{R }^{n}$$Rn. Michor, Peter W.; Mumford, David // Annals of Global Analysis & Geometry;Dec2013, Vol. 44 Issue 4, p529 

    We consider the groups $${\mathrm{Diff }}_\mathcal{B }(\mathbb{R }^n)$$ Diff B ( R n ) , $${\mathrm{Diff }}_{H^\infty }(\mathbb{R }^n)$$ Diff H ∞ ( R n ) , and $${\mathrm{Diff }}_{\mathcal{S }}(\mathbb{R }^n)$$ Diff S ( R n ) of smooth diffeomorphisms on $$\mathbb{R }^n$$ R n which differ...

  • Moduli of bundles over rational surfaces and elliptic curves I: Simply laced cases. Leung, Naichung Conan; Jiajin Zhang // Journal of the London Mathematical Society;Dec2009, Vol. 80 Issue 3, p750 

    It is well known that del Pezzo surfaces of degree 9 − n one-to-one correspond to flat En bundles over an elliptic curve. In this paper, we construct ADE-bundles over a broader class of rational surfaces that we call ADE-surfaces, and extend the above correspondence to all flat G-bundles...

  • Canonical endomorphism field on a Lie algebra. Kocik, Jerzy // Journal of Generalized Lie Theory & Applications;Sep2010, Vol. 4 Issue 3, p1 

    We show that every Lie algebra is equipped with a natural (1, 1)-variant tensor field, the "canonical endomorphism field", determined by the Lie structure, and satisfying a certain Nijenhuis bracket condition. This observation may be considered as complementary to the Kirillov-Kostant-Souriau...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics