相关论文: Polarizing Anisotropic Heisenberg Groups
In this note we present a short alternative proof for the Bernstein problem in the three-dimensional Heisenberg group ${\rm Nil}_3$ by using the loop group technique.
The conditions under which a linear anisotropic polarization element orthogonalizes several polarization states of input totally polarized light were studied in the paper. The criterion for orthogonalization was obtained in the form of…
We study Lp-improving properties as well as the type set of certain singular measures on the Heisenberg group.
A categorification of the Heisenberg algebra is constructed in by Khovanov using graphical calculus, and left with a conjecture on the isomorphism between the Heisenberg algebra and Grothendieck ring of the constructed category. We give a…
The bracket map was originally considered for locally compact abelian groups. In this work we extend the study of bracket maps to the noncommutative setting, providing characterizations of bases and frames for cyclic subspaces of the…
We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We note that the operation used in knot-theoretic flocks has…
In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly…
Recent spectropolarimetric observations of Herbig AeBe stellar systems show linear polarization variability with wavelength and epoch near their obscured H-alpha emission. Surprisingly, this polarization is not coincident with the H-alpha…
We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we…
Let $G$ be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of $G$ has a nonuniqueness phase, in which there are infinitely many infinite clusters. This generalizes Hutchcroft's result for…
In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we provide the examples of the Lie algebra of the group…
In this article we describe extensions of some K-theory classes of Heisenberg modules over higher-dimensional noncommutative tori to projective modules over crossed products of noncommutative tori by finite cyclic groups, aka noncommutative…
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…
We study the light scattering of homogenous radially-anisotropic spherical particles. It is shown that radial anisotropy can be employed to tune effectively the electric resonances, and thus enable flexible overlapping of electric and…
We establish endpoint estimates for a class of oscillating spectral multipliers on Lie groups of Heisenberg type. The analysis follows an earlier argument due to the second and fourth author but requires the detailed analysis of the wave…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…
In this paper we are mainly concerned with the study of polarizations (in general of higher-order type) on a connected Lie group with a U(1)-principal bundle structure. The representation technique used here is formulated on the basis of a…
We have classified, upto isoclinism, certain groups with a given central factor. As an application, we classify, upto isoclinism, groups having at the most nine element centralizers. Among other results of independent interest, we have…
The goal of this paper is to present a number of problems about automorphism groups of nonpositively curved polyhedral complexes and their lattices, meant to highlight possible directions for future research.