R2-planes with 3-dimensional automorphism group fixing precisely a line

1983 ◽  
Vol 21 (1) ◽  
pp. 66-96 ◽  
Author(s):  
Hansjoachim Groh ◽  
Martin F. Lippert ◽  
Hans -Joachim Pohl
Keyword(s):  
Automorphism Group ◽  
3 Dimensional

scholarly journals On the classification of 3-dimensionalSL2(ℂ)-varieties

2000 ◽  
Vol 157 ◽  
pp. 129-147 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Semisimple Group ◽  
Picard Number ◽  
Projective Varieties ◽  
3 Dimensional

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

Some Minkowski planes with 3-dimensional automorphism group

1985 ◽  
Vol 25 (1) ◽  
pp. 88-100 ◽  
Author(s):  
G�nter F. Steinke
Keyword(s):  
Automorphism Group ◽  
Minkowski Planes ◽  
3 Dimensional

scholarly journals Relatively minimal quasihomogeneous projective 3-folds

2000 ◽  
Vol 157 ◽  
pp. 149-176 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Projective Varieties ◽  
3 Dimensional ◽  
Complex Projective

In the present work we classify the relatively minimal 3-dimensional quasihomogeneous complex projective varieties under the assumption that the automorphism group is not solvable. By relatively minimal we understand varietiesXhaving at most ℚ-factorial terminal singularities and allowing an extremal contractionX→Ywhere dimY< 3.

Automorphism groups of 3-dimensional complex tori

1999 ◽  
Vol 1999 (508) ◽  
pp. 99-125 ◽  
Author(s):  
Ch Birkenhake ◽  
V González ◽  
H Lange
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Three Dimensional ◽  
Maximal Order ◽  
3 Dimensional ◽  
Complex Tori

Abstract We compute all finite automorphism groups of three-dimensional complex tori which are maximal in the isogeny class. The maximal order of such an automorphism group is 1296.

scholarly journals Hyperbolic 2–dimensional manifolds with 3–dimensional automorphism group

2008 ◽  
Vol 12 (2) ◽  
pp. 643-711 ◽  
Author(s):  
Alexander V Isaev
Keyword(s):  
Automorphism Group ◽  
3 Dimensional

scholarly journals On Low-Dimensional Complex ω-Lie Superalgebras

2021 ◽  
Author(s):  
Jia Zhou ◽  
Liangyun Chen
Keyword(s):  
Automorphism Group ◽  
Representation Theory ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
3 Dimensional ◽  
Finite Dimensional ◽  
Low Dimensional ◽  
Derivation Superalgebra

Abstract Let (g, [−, −], ω) be a finite-dimensional complex ω-Lie superalgebra. In this paper, we introduce the notions of derivation superalgebra Der(g) and the automorphism group Aut(g) of (g, [−, −], ω). We study Derω (g) and Autω (g), which are superalgebra of Der(g) and subgroup of Aut(g), respectively. For any 3-dimensional or 4-dimensional complex ω-Lie superalgebra g, we explicitly calculate Der(g) and Aut(g), and obtain Jordan standard forms of elements in the two sets. We also study representation theory of ω-Lie superalgebras and give a conclusion that all nontrivial non-ω-Lie 3-dimensional and 4-dimensional ω-Lie superalgebras are multiplicative, as well as we show that any irreducible respresentation of the 4-dimensional ω-Lie superalgebra P2,k(k 6= 0, −1) is 1-dimensional.

scholarly journals Automorphisms of a Clifford-like parallelism

2021 ◽  
Vol 21 (1) ◽  
pp. 63-73
Author(s):  
Hans Havlicek ◽  
Stefano Pasotti ◽  
Silvia Pianta
Keyword(s):  
Automorphism Group ◽  
Skew Field ◽  
3 Dimensional ◽  
Skew Fields ◽  
Double Space

Abstract We focus on the description of the automorphism group Γ∥ of a Clifford-like parallelism ∥ on a 3-dimensional projective double space (ℙ(HF ), ∥ ℓ , ∥ r ) over a quaternion skew field H (of any characteristic). We compare Γ∥ with the automorphism group Γ ℓ of the left parallelism ∥ ℓ , which is strictly related to Aut(H). We build up and discuss several examples showing that over certain quaternion skew fields it is possible to choose ∥ in such a way that Γ∥ is either properly contained in Γ ℓ or coincides with Γ ℓ even though ∥ ≠ ∥ ℓ .

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

Deviations from Ideal Decagonal Symmetry in Electron Diffraction Patterns of the “Decagonal” Phase in the Al-Co-Cu Alloy System

1991 ◽  
Vol 49 ◽  
pp. 914-915
Author(s):  
Atul S. Ramani ◽  
Earle R. Ryba ◽  
Paul R. Howell
Keyword(s):  
Electron Microscope ◽  
Alloy System ◽  
Nominal Composition ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Decagonal Phase ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Lattice Periodicity ◽  
Diffraction Patterns

The “decagonal” phase in the Al-Co-Cu system of nominal composition Al65CO15Cu20 first discovered by He et al. is especially suitable as a topic of investigation since it has been claimed that it is thermodynamically stable and is reported to be periodic in the dimension perpendicular to the plane of quasiperiodic 10-fold symmetry. It can thus be expected that it is an important link between fully periodic and fully quasiperiodic phases. In the present paper, we report important findings of our transmission electron microscope (TEM) study that concern deviations from ideal decagonal symmetry of selected area diffraction patterns (SADPs) obtained from several “decagonal” phase crystals and also observation of a lattice of main reflections on the 10-fold and 2-fold SADPs that implies complete 3-dimensional lattice periodicity and the fundamentally incommensurate nature of the “decagonal” phase. We also present diffraction evidence for a new transition phase that can be classified as being one-dimensionally quasiperiodic if the lattice of main reflections is ignored.

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