The structure of homomorphisms of connected locally compact groups into compact groups

Abstract

The crystallization, microstructure, and soft magnetic properties of Fe 52 Co 34 Hf 7 B 6 Cu 1 alloy are studied. Amorphous Fe 52 Co 34 Hf 7 B 6 Cu 1 alloys are first treated by a pulsed magnetic field with a medium frequency, and then annealed at 100 • C-400 • C for 30 min in a vacuum. The rise in temperature during the treatment by a pulsed magnetic field is measured by a non-contact infrared thermometer. The soft magnetic properties of specimens are measured by a vibrating sample magnetometer (VSM). The microstructure changes of specimens are observed by a Mössbauer spectroscopy and transmission electron microscope (TEM). The results show the medium-frequency pulsating magnetic field will promote nanocrystallization of the amorphous alloy with a lower temperature rise. The nanocrystalline phase is α-Fe(Co) with bcc crystal structure, and the grain size is about 10 nm. After vacuum annealing at 100 • C for 30 min, scattering nanocrystalline phases become more uniform, the coercive force and the saturation magnetization of the specimens are 41.98 A/m and 185.15 emu/g.

Automatic Continuity of Abstract Homomorphisms Between Locally Compact and Polish Groups

“…We finally remark that the first paragraphs in [Sht2] might give the erroneous impression that [Kra,Theorem 18] is incorrect, and that [Kra,Theorem 11] is implied by the author's earlier work on locally bounded homomorphisms.…”

Строение Локально Ограниченных Конечномерных Представлений Связных Локально Компактных Групп

“…многими авторами (см., например, [3]- [13] и приведенную в этих статьях библиографию), но результаты перечисленных работ связаны либо с условием плотности образа соответствующего отображения, либо с условием алгебраичности рассматриваемых групп, так что эти результаты нельзя непосредственно применить к изучению конечномерных представлений общих связных групп Ли и тем более общих связных локально компактных групп. Более подробное изложение истории вопроса приведено в [14], где с помощью более ранних результатов автора [15] об автоматической непрерывности локально ограниченных конечномерных линейных представлений связных групп Ли был получен ряд результатов, относящихся к (не обязательно непрерывным) конечномерным унитарным представлениям связных локально компактных групп.…”

Connected locally compact groups: The Hochschild kernel and faithfulness of locally bounded finite-dimensional representations

“…We recall the description of the intersection of the kernels of continuous finite-dimensional unitary representations (the von Neumann kernel) and the intersection of the kernels of all (not necessarily continuous) finite-dimensional unitary representations ("the smallest von Neumann kernel") of a locally compact group [24]. Let H = H(G) be the analytic subgroup of a connected locally compact group G generated by all the noncompact simple analytic subgroups of G. An example of a connected reductive Lie group G with vNk(G) = svNk(G) is also given in [24].…”

“…Using these, in [24] we obtained a number of results on the structure of homomorphisms taking connected locally compact groups into compact groups. In this paper we consider applying the results in [9] to study the question of the existence of a faithful locally bounded (not necessarily continuous) finite-dimensional linear representation of a given locally compact group and to give a description of the Hochschild kernel urk(G) of a given locally compact group G (or of the intersection of the kernels of continuous finite-dimensional linear representations of a topological group G).…”