scholarly journals On the construction of $ \mathbb Z^n_2- $grassmannians as homogeneous $ \mathbb Z^n_2- $spaces

2021 ◽  
Vol 30 (1) ◽  
pp. 221-241
Author(s):  
Mohammad Mohammadi ◽  
◽  
Saad Varsaie
Keyword(s):  
Lie Group ◽  
Explicit Description ◽  
Functor Of Points

<abstract><p>In this paper, we construct the $ \mathbb Z^n_2- $grassmannians by gluing of the $ \mathbb Z^n_2- $domains and give an explicit description of the action of the $ \mathbb Z^n_2- $Lie group $ GL(\overrightarrow{\textbf{m}}) $ on the $ \mathbb Z^n_2- $grassmannian $ G_{ \overrightarrow{\textbf{k}}}(\overrightarrow{\textbf{m}}) $ in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the $ \mathbb Z^n_2- $grassmannian.</p></abstract>

On the construction of supergrassmannians as homogeneous superspaces

2020 ◽  
pp. 2150053
Author(s):  
Mohammad Mohammadi ◽  
Saad Varsaie
Keyword(s):  
Lie Group ◽  
Explicit Description ◽  
Functor Of Points

In this paper, we give an explicit description of the action of the super Lie group [Formula: see text] on supergrassmannian [Formula: see text] in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the supergrassmannian.

Description of reflection-generated polytopes using decorated Coxeter diagrams

1995 ◽  
Vol 73 (9-10) ◽  
pp. 566-584 ◽  
Author(s):  
B. Champagne ◽  
M. Kjiri ◽  
J. Patera ◽  
R. T. Sharp
Keyword(s):  
Symmetry Group ◽  
Weyl Group ◽  
Lie Group ◽  
Single Point ◽  
Explicit Description ◽  
New Method ◽  
Maximal Dimension ◽  
Group D

A new method of explicit description of n-dimensional polytopes generated by reflections of a single point (D-polytopes) or a face of maximal dimension (V-polytopes) is used to provide a comprehensive uniform description of all such polytopes in dimensions three and four. In addition a class of six-dimensional polytopes is also described; its symmetry group is the Weyl group of the simple Lie group D6.

The Movement of Ezekiel’s “Living Beings” in 4Q405 Shirot ‘Olat Hashabbat. Part II: The Twelfth Song

2018 ◽  
Vol 27 (1) ◽  
Author(s):  
Annette Evans
Keyword(s):  
Explicit Description ◽  
Plural Form ◽  
The Law ◽  
Mount Sinai

In this article descriptions of angelic movement in the Twelfth Song are compared to descriptions of such activity arising from the throne of God in Ezekiel’s vision in Ezekiel 1 and 10, and to that in the Seventh Song as contained in scroll 4Q403. The penultimate Twelfth Song of the Songs of the Sabbath Sacrifice culminates in a more explicit description of angelic messenger activity and in other nuances. The Twelfth Song was intended to be read on the Sabbath immediately following Shavu’ot, when the traditional synagogue reading is Ezekiel 1 and Exodus 19–20. The possible significance for the author of Songs of the Sabbath Sacrifice of the connection between the giving of the Law at Mount Sinai and Ezekiel’s vision where merkebah thrones and seats appear in the plural form is considered in the conclusion

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

ε‎-Invariance

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Algebra ◽  
Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

The Centralizer

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Group ◽  
Group Structure ◽  
Diffeomorphism Group ◽  
Group Diff ◽  
Local Solutions

The pseudogroup of local solutions in Chapter 3 defines another pseudogroup by taking its centralizer inside the diffeomorphism group Diff(M) of a manifold M. These two pseudogroups define a Lie group structure on M.

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

scholarly journals The Second Lie-Group $SO_o(n,1)$ Used to Solve Ordinary Differential Equations

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Chein-Shan Liu ◽  
Wun-Sin Jhao
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group
Sign in / Sign up

Export Citation Format

Share Document