Semantic.
© by Thierry PERIAT: The Theory of the (E) question – Semantic
Items 
Peculiar terms 
Details Comments 

Products and their extensions 
Tensor product 
See any good book. The operator is denoted Ä(…, …) 

Projectile 
First argument: Ä(Projectile, …) 

Target 
Second argument: Ä(…, Target) 

Cube 


Symmetric


Antisymmetric


Reduced


Antireduced


Symmetric and reduced 

Antisymmetric and antireduced 

Null 

Hypercube 
A hypercube is a generalization of the concept of cube to a space with a physical dimension greater than three. 

Deformed tensor product 
A deformed tensor product is a classical tensor product that has been deformed by a cube


Deformed exterior product 


Deformed Lie product 
A deformed Lie product is a deformed exterior product built on an antisymmetric cube 

Elements of a decomposition 
Intrinsic ingredients 


Main part 
([P], …) is the main part in a decomposition ([P], z). This is an element of M(D, K) 

Residual part 
(…, z) is the residual part in a decomposition ([P], z); this is an element in E(D, K) 

Trivial 
A decomposition is said to be trivial when: Ä_{A}(a, b) > = [P]. b > + 0 > 

Nontrivial 
A decomposition is nontrivial when its residual part doesn’t vanish. 

Methods of decomposition 
An intrinsic method of decomposition is a mathematical method allowing the discovery of one or several pair(s) ([P], z) with the help of intrinsic ingredients only. Up to now, I have only done in in a threedimensional context for deformed Lie products. 

An extrinsic method of decomposition is any mathematical method offering an answer to the (E) question with the help of ingredients which are not only intrinsic to the question. 

Russian dolls 
The Russian dolls method is inspired by the wellknown traditional objects and describes any procedure allowing the discovery of decompositions when the (E) question is asked in E(D + 1, K) but has been answered in E(D, K). 
© Thierry PERIAT
Go back to the chapter: "Mathematical methods".
Date de dernière mise à jour : 11/05/2022