Search results for " mathematical physics"
showing 10 items of 396 documents
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.
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 $\le 5$.
Logarithmic Vector Fields and the Severi Strata in the Discriminant
2017
The discriminant, D, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta invariants of the singular points of the fibre. The members of the partition are known as the Severi strata. The smallest is the δ-constant stratum, D(δ), where the genus of the fibre is 0. It is well known, by work of Givental’ and Varchenko, to be Lagrangian with respect to the symplectic form Ω obtained by pulling back the intersection form on the cohomology of the fibre via the period mapping. We show that the remaining Severi strata are also co-isotropic with respect to Ω, and mor…
A characterization of fundamental algebras through S-characters
2020
Abstract Fundamental algebras play an important role in the theory of algebras with polynomial identities in characteristic zero. They are defined in terms of multialternating polynomials non vanishing on them. Here we give a characterization of fundamental algebras in terms of representations of symmetric groups obtaining this way an equivalent definition. As an application we determine when a finitely generated Grassmann algebra is fundamental.
Specht property for some varieties of Jordan algebras of almost polynomial growth
2019
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A 1 , a suitable infinitely generated metabelian Jordan algebra defined in [27] .
Entropy, Lyapunov exponents, and rigidity of group actions
2018
This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number of classical tools in smooth ergodic theory -- particularly Lyapunov exponents and metric entropy -- as tools to study rigidity properties of group actions on manifolds. We do not present comprehensive treatment of group actions or general rigidity programs. Rather, we focus on two rigidity results in higher-rank dynamics: the measure rigidity theorem for affine Anosov abelian actions on tori due to A. Katok and R. Spatzier [Ergodic Theory Dynam. Systems…
Approximation by uniform domains in doubling quasiconvex metric spaces
2020
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
Nowhere differentiable intrinsic Lipschitz graphs
2021
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.