321 research outputs found
Dimension expanders
We show that there exists k \in \bbn and 0 < \e \in\bbr such that for
every field of characteristic zero and for every n \in \bbn, there exists
explicitly given linear transformations satisfying
the following:
For every subspace of of dimension less or equal ,
\dim(W+\suml^k_{i=1} T_iW) \ge (1+\e) \dim W. This answers a question of Avi
Wigderson [W]. The case of fields of positive characteristic (and in particular
finite fields) is left open
Classification of Lie bialgebras over current algebras
In the present paper we present a classification of Lie bialgebra structures
on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional
Lie algebra.Comment: 26 page
A remark on simplicity of vertex algebras and Lie conformal algebras
I give a short proof of the following algebraic statement: if a vertex
algebra is simple, then its underlying Lie conformal algebra is either abelian,
or it is an irreducible central extension of a simple Lie conformal algebra.Comment: 6 pages. Some typos corrected. Removed a wrongly stated associativity
propert
Incorporation of Spacetime Symmetries in Einstein's Field Equations
In the search for exact solutions to Einstein's field equations the main
simplification tool is the introduction of spacetime symmetries. Motivated by
this fact we develop a method to write the field equations for general matter
in a form that fully incorporates the character of the symmetry. The method is
being expressed in a covariant formalism using the framework of a double
congruence. The basic notion on which it is based is that of the geometrisation
of a general symmetry. As a special application of our general method we
consider the case of a spacelike conformal Killing vector field on the
spacetime manifold regarding special types of matter fields. New perspectives
in General Relativity are discussed.Comment: 41 pages, LaTe
Groups with identities
This is a survey of a still evolving subject. The purpose is to develop a theory of prounipotent (respectively pro-) groups satisfying a prounipotent (respectively pro-) identity that is parallel to the theory of PI-algebra
Split structures in general relativity and the Kaluza-Klein theories
We construct a general approach to decomposition of the tangent bundle of
pseudo-Riemannian manifolds into direct sums of subbundles, and the associated
decomposition of geometric objects. An invariant structure {\cal H}^r defined
as a set of r projection operators is used to induce decomposition of the
geometric objects into those of the corresponding subbundles. We define the
main geometric objects characterizing decomposition. Invariant non-holonomic
generalizations of the Gauss-Codazzi-Ricci's relations have been obtained. All
the known types of decomposition (used in the theory of frames of reference, in
the Hamiltonian formulation for gravity, in the Cauchy problem, in the theory
of stationary spaces, and so on) follow from the present work as special cases
when fixing a basis and dimensions of subbundles, and parameterization of a
basis of decomposition. Various methods of decomposition have been applied here
for the Unified Multidimensional Kaluza-Klein Theory and for relativistic
configurations of a perfect fluid. Discussing an invariant form of the
equations of motion we have found the invariant equilibrium conditions and
their 3+1 decomposed form. The formulation of the conservation law for the curl
has been obtained in the invariant form.Comment: 30 pages, RevTeX, aps.sty, some additions and corrections, new
references adde
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