scholarly journals Infinite approximate subgroups of soluble Lie groups

2021 ◽  
Author(s):  
Simon Machado
Keyword(s):  
Lie Groups ◽  
Structure Theorem ◽  
Quasi Crystals

AbstractWe study infinite approximate subgroups of soluble Lie groups. We show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building upon this result we prove a structure theorem for approximate lattices in soluble Lie groups. This extends to soluble Lie groups a theorem about quasi-crystals due to Yves Meyer.

A Structure Theorem for Actions of Semisimple Lie Groups

2002 ◽  
Vol 156 (2) ◽  
pp. 565 ◽  
Author(s):  
Amos Nevo ◽  
Robert J. Zimmer
Keyword(s):  
Lie Groups ◽  
Structure Theorem ◽  
Semisimple Lie Groups

A Structural Model for a Quasi-Crystalline Material Derived from TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 48-49
Author(s):  
Jan-Olov Bovin ◽  
Osamu Terasaki ◽  
Jan-Olle Malm ◽  
Sven Lidin ◽  
Sten Andersson
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Structural Model ◽  
Image Intensifier ◽  
Crystalline Materials ◽  
Icosahedral Phases ◽  
Transmission Electron ◽  
Electron Microscopes ◽  
Diffraction Patterns ◽  
Quasi Crystals

High resolution transmission electron microscopy (HRTEM) is playing an important role in identifying the new icosahedral phases. The selected area diffraction patterns of quasi crystals, recorded with an aperture of the radius of many thousands of Ångströms, consist of dense arrays of well defined sharp spots with five fold dilatation symmetry which makes the interpretation of the diffraction process and the resulting images different from those invoked for usual crystals. The atomic structure of the quasi crystals is not established even if several models are proposed. The correct structure model must of course explain the electron diffraction patterns with 5-, 3- and 2-fold symmetry for the phases but it is also important that the HRTEM images of the alloys match the computer simulated images from the model. We have studied quasi crystals of the alloy Al65Cu20Fe15. The electron microscopes used to obtain high resolution electro micrographs and electron diffraction patterns (EDP) were a (S)TEM JEM-2000FX equipped with EDS and PEELS showing a structural resolution of 2.7 Å and a IVEM JEM-4000EX with a UHP40 high resolution pole piece operated at 400 kV and with a structural resolution of 1.6 Å. This microscope is used with a Gatan 622 TV system with an image intensifier, coupled to a YAG screen. It was found that the crystals of the quasi crystalline materials here investigated were more sensitive to beam damage using 400 kV as electron accelerating voltage than when using 200 kV. Low dose techniques were therefore applied to avoid damage of the structure.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras

ELECTRON DIFFRACTION AND MICROSCOPY OF INCOMMENSURATE PHASES AND QUASI-CRYSTALS

1986 ◽  
Vol 47 (C3) ◽  
pp. C3-437-C3-446 ◽  
Author(s):  
J. W. STEEDS ◽  
R. AYER ◽  
Y. P. LIN ◽  
R. VINCENT
Keyword(s):  
Electron Diffraction ◽  
Quasi Crystals ◽  
Incommensurate Phases

Electronic conductivity of icosahedral quasi-crystals

2002 ◽  
Vol 172 (2) ◽  
pp. 233 ◽  
Author(s):  
Yurii Kh. Vekilov
Keyword(s):  
Electronic Conductivity ◽  
Quasi Crystals

Existence

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Structure Theorem ◽  
Quadratic Extension ◽  
Quadratic Space ◽  
Division Algebras ◽  
Separable Extension ◽  
Valued Fields ◽  
Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

On Lattice-Ordered Rees Matrix Γ-Semigroups

2013 ◽  
Vol 59 (1) ◽  
pp. 209-218 ◽  
Author(s):  
Kostaq Hila ◽  
Edmond Pisha
Keyword(s):  
Structure Theorem ◽  
Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

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