# Definable groups and compact p-adic Lie groups

## 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 Isaacsâ€“Malleâ€“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 â‰¥ 2 and A be a free abelian Lie algebra of rank m â‰¥ 2. We prove that the test rank of the abelian product F Ã— 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 âˆž ( 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 âˆ’ 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...