Dimension expanders

We show that there exists k \in \bbn and 0 < \e \in\bbr such that for every field $F$ of characteristic zero and for every n \in \bbn, there exists explicitly given linear transformations $T_1,..., T_k: F^n \to F^n$ satisfying the following: For every subspace $W$ of $F^n$ of dimension less or equal $\frac n2$, \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

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

The ranks of central factor and commutator groups

The Schur Theorem says that if $G$ is a group whose center $Z(G)$ has finite index $n$, then the order of the derived group $G'$ is finite and bounded by a number depending only on $n$. In the present paper we show that if $G$ is a finite group such that $G/Z(G)$ has rank $r$, then the rank of $G'$ is $r$-bounded. We also show that a similar result holds for a large class of infinite groups

Hawking Radiation as Tunneling: the D-dimensional rotating case

The tunneling method for the Hawking radiation is revisited and applied to the $D$ dimensional rotating case. Emphasis is given to covariance of results. Certain ambiguities afflicting the procedure are resolved.Comment: Talk delivered at the Seventh International Workshop Quantum Field Theory under the influence of External Conditions, QFEXT'05, september 05,Barcelona, Spain. To appear in Journal of Phys.

Nonsoluble and non-p-soluble length of finite groups

Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. We prove that λ(G) is bounded in terms of the maximum 2-length of soluble subgroups of G, and that λ(G) is bounded by the maximum Fitting height of soluble subgroups. For an odd prime p, the non-p-soluble length λ p (G) is introduced, and it is proved that λ p (G) does not exceed the maximum p-length of p-soluble subgroups. We conjecture that for a given prime p and a given proper group variety V the non-p-soluble length λ p (G) of finite groups G whose Sylow p-subgroups belong to V is bounded. In this paper we prove this conjecture for any variety that is a product of several soluble varieties and varieties of finite exponent. As an application of the results obtained, an error is corrected in the proof of the main result of the second author’s paper Multilinear commutators in residually finite groups, Israel Journal of Mathematics 189 (2012), 207–224

On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type

The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions with the problem of quntization of hydrodynamics brackets is demonstrated

Trialogue on the number of fundamental constants

This paper consists of three separate articles on the number of fundamental dimensionful constants in physics. We started our debate in summer 1992 on the terrace of the famous CERN cafeteria. In the summer of 2001 we returned to the subject to find that our views still diverged and decided to explain our current positions. LBO develops the traditional approach with three constants, GV argues in favor of at most two (within superstring theory), while MJD advocates zero.Comment: Version appearing in JHEP; 31 pages late