scholarly journals Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Group Symmetry ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Lie Group Symmetry

The authors wish to make the following corrections to their paper [...]

scholarly journals New Type Direction Curves in 3-Dimensional Compact Lie Group

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 387 ◽  
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Normal Direction ◽  
General Definition ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Definition Of

In this paper, new types of associated curves, which are defined as rectifying-direction, osculating-direction, and normal-direction, in a three-dimensional Lie group G are achieved by using the general definition of the associated curve, and some characterizations for these curves are obtained. Additionally, connections between the new types of associated curves and the curves, such as helices, general helices, Bertrand, and Mannheim, are given.

scholarly journals THREE-POINT FUNCTIONS IN CONFORMAL FIELD THEORY WITH AFFINE LIE GROUP SYMMETRY

1999 ◽  
Vol 14 (08) ◽  
pp. 1225-1259 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Group ◽  
General Procedure ◽  
Group Symmetry ◽  
Conformal Field ◽  
Highest Weight ◽  
Integer Solutions ◽  
Lie Group Symmetry ◽  
General Method

In this paper we develop a general method for constructing three-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on two-point functions. The results are provided in terms of triangular coordinates used in a wave function description of vectors in highest weight modules. In this framework, complicated couplings translate into ordinary products of certain elementary polynomials. The discussions pertain to all simple Lie groups and arbitrary integrable representation. An interesting by-product is a general procedure for computing tensor product coefficients, essentially by counting integer solutions to certain inequalities. As an illustration of the construction, we consider in great detail the three cases SL(3), SL(4) and SO(5).

scholarly journals Lie group symmetry analysis for granular media stress equations

2005 ◽  
Vol 301 (1) ◽  
pp. 135-157 ◽  
Author(s):  
I. Kenneth Johnpillai ◽  
Scott W. McCue ◽  
James M. Hill
Keyword(s):  
Lie Group ◽  
Granular Media ◽  
Symmetry Analysis ◽  
Group Symmetry ◽  
Lie Group Symmetry
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