34 research outputs found
Central filtrations of Lie algebras
No full textConsider L to be a graded free Lie algebra over a principal ideal domain, and r a nonzero element of L such that its leading term s, i.e. its homogeneous component of highest order, is not a proper multiple. The main result we show in this thesis is that the graded ideal of leading terms of elements in R = (r) is equal to the ideal generated by the element s. As a consequence we prove that the center of L/R is trivial if the rank of the free Lie algebra L is greater than two
Mild pro-2-groups and 2-extensions of Q with restricted ramification
No full textAbstractUsing the mixed Lie algebras of Lazard, we extend the results of the first author on mild groups to the case p=2. In particular, we show that for any finite set S0 of odd rational primes we can find a finite set S of odd rational primes containing S0 such that the Galois group of the maximal 2-extension of Q unramified outside S is mild. We thus produce a projective system of such Galois groups which converge to the maximal pro-2-quotient of the absolute Galois group of Q unramified at 2 and ∞. Our results also allow results of Alexander Schmidt on pro-p-fundamental groups of marked arithmetic curves to be extended to the case p=2 over a global field which is either a function field of characteristic ≠2 or a totally imaginary number field
A sharp Bogomolov-type bound
No full textWe prove a sharp lower bound for the essential minimum of a nontranslate variety in certain abelian varieties. This uses and generalises a result of Galateau. Our bound is a new step in the direction of an abelian analogue by David and Philippon of a toric conjecture of Amoroso and David and has applications in the framework of anomalous intersections
On the descending central series of groups with a single defining relation
No full textAbstractIn this paper we show that the Lie algebra associated to the descending central series of a finitely generated group with a single “primitive” defining relation is a Lie algebra with a single defining relation. The proof uses results of [1]
The Genesis of a Theorem
No full textIn this article we trace the genesis of a theorem that gives for the first time examples of Galois group of the maximal -extension of , unramified outside a finite set of primes not containing , that are of cohomological dimension . The pro--group is a fab pro--group which means that all its derived factors are finite
Medea or the disorden in Neil Labute's "Medea Redux"
No full textEn el marco de las investigaciones sobre la recepción de Medea en la literatura y las
artes, el presente artículo presenta un estudio de la obra teatral Medea Redux,
reescritura de la Medea de Eurípides del controvertido dramaturgo norteamericano
Neil Labute (1999). Mediante un análisis comparativo entre los textos de ambos
autores se estudian los procedimientos mediante los cuales Labute se "apropia" del
mythos antiguo, para concluir sobre qué aspectos interesan al dramaturgo
contemporáneo y en qué ámbitos innova, tanto en lo que se refiere a la propia
narración del relato mítico y a la caracterización de los personajes, como a la
eliminación o conservación de ciertos aspectos formales presentes en la tragedia
antigua. Igualmente se establece una conexión entre el teatro de Labute -en Medea
Redux pero también en Helter Skelter, pieza de 2008 inspirada igualmente en Medea y el trasfondo moral de la tragedia euripidea.Within the research on reception of Medea in Literature and Art, this paper studies the
play Medea Redux, a recreation of Euripides' Medea by the controversial American
playwright Neil Labute (1999). Through a comparative analysis between Labute's and
Euripides' texts, the procedures followed by Labute to 'appropriate' the ancient
mythos are studied, in order to conclude on the aspects that interest the modern
author and on the areas in which he innovates. This is done both in terms of the
mythical story itself and the characters, and in terms of the elimination or
conservation of certain formal aspects of the ancient tragedy. A connection is also
established between Labute's theatre (in Medea Redux but also in Helter Skelter, a
2008 play also inspired by the Greek Medea) and the moral background of the
Euripidean Tragedy
Free Lie algebras as modules over their enveloping algebras
No full textIn this paper we determine the linear relations that exist between the free generators of a free Lie algebra L when it is viewed as a module over its enveloping algebra via the adjoint representation. As an application, the annihilator of a homogeneous element of L is determined.</p
The lower central series of the group ⟨𝑥,𝑦: 𝑥^{𝑝}=1⟩
No full textIn this paper we determine the Lie algebra associated to the lower central series of the group
⟨
x
,
y
:
x
p
=
1
⟩
\langle x,y:{x^p} = 1\rangle
, p a prime.</p
