scholarly journals AFFINE PARTICLES AND FIELDS

2005 ◽  
Vol 02 (02) ◽  
pp. 189-201 ◽  
Author(s):  
DJORDJE ŠIJAČKI
Keyword(s):  
Symmetry Group ◽  
Semidirect Product ◽  
Linear Transformations ◽  
Infinite Matrices ◽  
Special Linear ◽  
3 Dimensional ◽  
Infinite Dimensional ◽  
Dimensional Spacetime ◽  
Affine Symmetry ◽  
Group A

The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in D ≥ 3 dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are presented. A Dirac-like affine equation, with infinite matrices generalizing the γ matrices, is constructed.

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

scholarly journals A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1259 ◽  
Author(s):  
Abraham A. Ungar
Keyword(s):  
Special Relativity ◽  
Symmetry Group ◽  
Lorentz Transformation ◽  
Lorentz Group ◽  
Transformation Group ◽  
Relativity Theory ◽  
Symmetry Violation ◽  
3 Dimensional ◽  
Dimensional Spacetime ◽  
The Common

A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

scholarly journals W∞ AND ANOMALIES OF SELF-DUAL EINSTEIN THEORIES

1991 ◽  
Vol 06 (20) ◽  
pp. 1893-1900
Author(s):  
V. G. J. RODGERS
Keyword(s):  
Symmetry Group ◽  
Effective Action ◽  
Central Extension ◽  
Quantum Deformation ◽  
3 Dimensional ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Group Of Symmetries

Recently it has been demonstrated that self-dual Einstein Euclidean instantons possess an infinite-dimensional group of symmetries which contain the standard w∞. Since w∞ has a central extension only in its w2 subalgebra one may claim that there is an anomaly in the symmetry group of these instantons which is described by a 3-dimensional w2 effective action. Thus one has a bosonization of the 3/2 spin anomaly of the Eguchi–Hanson instantons. In analogy to w∞ we construct the 3-dimensional effective action for the Lone Star W∞ algebra. This suggests that there is a quantum deformation of the instantons that contributes to the effective action of 4-dimensional self-dual gravity. We comment on this possibility.

Lie subgroups of the symmetry group of the equations describing a nonstationary and isentropic flow: Invariant and partially invariant solutions

1994 ◽  
Vol 72 (7-8) ◽  
pp. 362-374 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Symmetry Group ◽  
Dimensional Space ◽  
Projective Group ◽  
Invariant Solutions ◽  
Partially Invariant Solutions ◽  
Isentropic Flow ◽  
Dimensional Space Time ◽  
Group A ◽  
Special Case

We study the symmetries of the equations describing a nonstationary and isentropic flow for an ideal and compressible fluid in four-dimensional space-time. We prove that this system of equations is invariant under the Galilean-similitude group. In the special case of the adiabatic exponent γ = 5/3, corresponding to a diatomic gas, the symmetry group of this system is larger. It is invariant under the Galilean-projective group. A representatives list of subalgebras of Galilean similitude and Galilean-projective Lie algebras, obtained by the method of classification by conjugacy classes under the action of their respective Lie groups, is presented. The results are given in a normalized list and summarized in tables. Examples of invariant and nonreducible partially invariant solutions, obtained from this classification, is constructed. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras for the Euler and magnetohydrodynamics equations.

scholarly journals A Novel Method to Enhance Dynamic Rhinoplasty Outcomes: Double “V” Carving for Alloplastic Grafts

2019 ◽  
Vol 99 (4) ◽  
pp. 262-267 ◽  
Author(s):  
Shan-shan Bai ◽  
Dong Li ◽  
Liang Xu ◽  
Hui-chuan Duan ◽  
Jie Yuan ◽  
...  
Keyword(s):  
Practical Method ◽  
Control Group ◽  
Augmentation Rhinoplasty ◽  
3 Dimensional ◽  
Asian Patients ◽  
Subjective Evaluations ◽  
Group A ◽  
Novel Method ◽  
Group B ◽  
And Control

Augmentation rhinoplasty is one of the most common plastic surgery procedures performed in Asia. Most Asian patients desire not only a natural-looking nose but also a nose with natural feel. Achieving such rhinoplasty outcomes with grafts has been a challenge for surgeons due to rigidity of grafting material. We propose a novel technique to address this limitation. A total of 200 healthy adult patients aged from 18 to 25 years were randomly chosen and classified into 5 groups: A, B, C, D, and control. Each group included 40 patients. The patients assigned to conventional grafting underwent rhinoplasty with L-shaped silicone prosthesis (group A) or expanded polytetrafluoroethylene (e-PTFE; group B), using traditional carving methods. The patients assigned to dynamic rhinoplasty underwent silicone (group C) or e-PTFE grafts (group D) using the modified double “V” method, which involves removing bilateral wedges from the graft to decrease rigidity. Patients in control group do not undergo the surgery. A 3-dimensional raster surface scanner was used to capture the images of the patients accurately and nasal mobility was measured. Subjective evaluations were carried out by a series of questionnaires asked to the patients. The angle α of nasal mobility was significantly lower in conventional grafting (23.09 [5.34] mm for silicone and 17.88 [4.96] mm for e-PTFE) versus the “V” carving (30.53 [3.76] mm for silicone and 23.77 [4.53] mm for e-PTFE; P < .05). The double “V” carving method is a simple, effective, and practical method for improving dynamic nasal outcomes in patient undergoing augmentation rhinoplasty.

scholarly journals Baer–Levi semigroups of linear transformations

2004 ◽  
Vol 134 (3) ◽  
pp. 477-499 ◽  
Author(s):  
Suzana Mendes-Gonçalves ◽  
R. P. Sullivan
Keyword(s):  
Vector Space ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Basic Properties ◽  
Maximal Subsemigroups ◽  
Linear Version ◽  
Infinite Set

Given an infinite-dimensional vector space V, we consider the semigroup GS (m, n) consisting of all injective linear α: V → V for which codim ran α = n, where dim V = m ≥ n ≥ ℵ0. This is a linear version of the well-known Baer–Levi semigroup BL (p, q) defined on an infinite set X, where |X| = p ≥ q ≥ ℵ0. We show that, although the basic properties of GS (m, n) are the same as those of BL (p, q), the two semigroups are never isomorphic. We also determine all left ideals of GS (m, n) and some of its maximal subsemigroups; in this, we follow previous work on BL (p, q) by Sutov and Sullivan as well as Levi and Wood.

scholarly journals A remark on the essential spectra of quasi-similar dominant contractions

1989 ◽  
Vol 31 (2) ◽  
pp. 165-168
Author(s):  
B. P. Duggal
Keyword(s):  
Complex Hilbert Space ◽  
Normal Extension ◽  
Inclusion Relation ◽  
Linear Transformations ◽  
Essential Spectra ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Hyponormal Operators ◽  
Image Position ◽  
Dominant Operator

We consider operators, i.e. bounded linear transformations, on an infinite dimensional separable complex Hilbert space H into itself. The operator A is said to be dominant if for each complex number λ there exists a number Mλ(≥l) such that ∥(A – λ)*x∥ ≤ Mλ∥A – λ)x∥ for each x∈H. If there exists a number M≥Mλ for all λ, then the dominant operator A is said to be M-hyponormal. The class of dominant (and JW-hyponormal) operators was introduced by J. G. Stampfli during the seventies, and has since been considered in a number of papers, amongst then [7], [11]. It is clear that a 1-hyponormal is hyponormal. The operator A*A is said to be quasi-normal if Acommutes with A*A, and we say that A is subnormal if A has a normal extension. It is known that the classes consisting of these operators satisfy the following strict inclusion relation:

scholarly journals Infinite-dimensional triangularizable algebras

2019 ◽  
Vol 31 (1) ◽  
pp. 19-33
Author(s):  
Zachary Mesyan
Keyword(s):  
Vector Space ◽  
Arbitrary Subset ◽  
Linear Transformations ◽  
Nilpotent Semigroup ◽  
Infinite Dimensional ◽  
Closed Fields ◽  
Algebraically Closed Fields ◽  
Basis Vectors

Abstract Let {\mathrm{End}_{k}(V)} denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define {X\subseteq\mathrm{End}_{k}(V)} to be triangularizable if V has a well-ordered basis such that X sends each vector in that basis to the subspace spanned by basis vectors no greater than it. We then show that an arbitrary subset of {\mathrm{End}_{k}(V)} is strictly triangularizable (defined in the obvious way) if and only if it is topologically nilpotent. This generalizes the theorem of Levitzki that every nilpotent semigroup of matrices is triangularizable. We also give a description of the triangularizable subalgebras of {\mathrm{End}_{k}(V)} , which generalizes a theorem of McCoy classifying triangularizable algebras of matrices over algebraically closed fields.

Presentations for 3-Dimensional Special Linear Groups Over Integer Rings

1992 ◽  
Vol 115 (1) ◽  
pp. 19
Author(s):  
Marston Conder ◽  
Edmund Robertson ◽  
Peter Williams
Keyword(s):  
Linear Groups ◽  
Special Linear ◽  
3 Dimensional ◽  
Special Linear Groups ◽  
Integer Rings

scholarly journals Invariant Poisson–Nijenhuis structures on Lie groups and classification

2018 ◽  
Vol 15 (04) ◽  
pp. 1850059 ◽  
Author(s):  
Zohreh Ravanpak ◽  
Adel Rezaei-Aghdam ◽  
Ghorbanali Haghighatdoost
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Symmetry Group ◽  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Text Structure ◽  
Baxter Equation ◽  
Text Structures ◽  
Group A

We study right-invariant (respectively, left-invariant) Poisson–Nijenhuis structures ([Formula: see text]-[Formula: see text]) on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra [Formula: see text]. We show that [Formula: see text]-[Formula: see text] structures can be used to find compatible solutions of the classical Yang–Baxter equation (CYBE). Conversely, two compatible [Formula: see text]-matrices from which one is invertible determine an [Formula: see text]-[Formula: see text] structure. We classify, up to a natural equivalence, all [Formula: see text]-matrices and all [Formula: see text]-[Formula: see text] structures with invertible [Formula: see text] on four-dimensional symplectic real Lie algebras. The result is applied to show that a number of dynamical systems which can be constructed by [Formula: see text]-matrices on a phase space whose symmetry group is Lie group a [Formula: see text], can be specifically determined.

Sign in / Sign up

Export Citation Format

Share Document