© 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 or, as first help: the extern link on Wikipedia – GB 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 
Intrinsic 
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. 

Extrinsic 
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, 07 January 2019.
To go further: Mathematical methods