Search results for "Mathematical physics"
showing 10 items of 2687 documents
Sobolev homeomorphic extensions onto John domains
2020
Abstract Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W 1 , 2 -extension but not even a homeomorphic W 1 , 1 -extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p 2 . John disks, being one sided quasidisks, are of fundamental importance in Geometric Function The…
Structure of the space of reducible connections for Yang-Mills theories
1990
Abstract The geometrical structure of the gauge equivalence classes of reducible connections are investigated. The general procedure to determine the set of orbit types (strata) generated by the action of the gauge group on the space of gauge potentials is given. In the so obtained classification, a stratum, containing generically certain reducible connections, corresponds to a class of isomorphic subbundles given by an orbit of the structure and gauge group. The structure of every stratum is completely clarified. A nonmain stratum can be understood in terms of the main stratum corresponding to a stratification at the level of a subbundle.
Linearization of complex hyperbolic Dulac germs
2021
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.
Hyperbolicity as an obstruction to smoothability for one-dimensional actions
2017
Ghys and Sergiescu proved in the $80$s that Thompson's group $T$, and hence $F$, admits actions by $C^{\infty}$ diffeomorphisms of the circle . They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of piecewise projective homeomorphisms, and Lodha-Moore defined finitely presentable groups of piecewise projective homeomorphisms. These groups are of particular interest because they are nonamenable and contain no free subgroup. In contrast to the result of Ghys-Sergiescu, we prove that the groups of Monod and Lodha-Moore are not topologically conjugate to a group of $C^1$ diffeomorphisms. Fur…
A quantitative isoperimetric inequality for fractional perimeters
2011
Abstract Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.
Unbounded C$^*$-seminorms and $*$-Representations of Partial *-Algebras
2009
The main purpose of this paper is to construct *-representations from unbounded C*-seminorms on partial *-algebras and to investigate their *-representations. © Heldermann Verlag.
Cohomology and Deformation of Leibniz Pairs
1995
Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra $A$ together with a Lie algebra $L$ mapped into the derivations of $A$. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.
Decomposition numbers and local properties
2020
Abstract If G is a finite group and p is a prime, we give evidence that the p-decomposition matrix encodes properties of p-Sylow normalizers.
On defects of characters and decomposition numbers
2017
We propose upper bounds for the number of modular constituents of the restriction modulo [math] of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.
On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
2019
We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for $t(\mathfrak{l}) \le 6$ and this allows us to represent $\mathfrak{l}$ when its dimension is $\le 5$.