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Friday, 29 June 2018

The Days of von Neumann Algebra 2015


The Days of von Neumann Algebra 
viz. The cited papers' texts are also shown at this site.

TANAKA Akio

1.
My study's turning point from intuitive essay to mathematical writing was at the days of learning von Neumann Algebra, that was written by four parts from von Neumann Algebra 1 to von Neumann Algebra 4. The days are about between 2006 and 2008, when I was thinking about switching over from intuitive to algebraic writing. The remarkable results of writing these papers were what the relation between infinity and finiteness in language was first able to clearly describe. Two papers of von Neumann 2, Property Infinite and Purely Infinite, were the trial to the hard theme of infinity in language.
The contents' titles are the following.

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von Neumann Algebra 

Assistant Site : sekinanlogos

TANAKA Akio

On Infinity of Language

von Neumann Algebra 1
von Neumann Algebra 2
von Neumann Algebra 3
von Neumann Algebra 4

References

Algebraic Linguistics 
Distance Theory Algebraically Supplemented
Noncommutative Distance Theory
Clifford AlgebraKac-Moody Lie Algebra
Operator Algebra

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2.
The papers of von Neumann Algebra and References are the next.

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von Neumann Algebra 1 

MeasureTensor ProductCompact Operator


von Neumann Algebra 2

1 Generation Theorem

von Neumann Algebra 3

1 Properly Infinite
2 Purely Infinite

von Neumann Algebra 4

Tomita's Fundamental Theorem
Borchers' Theorem

Algebraic Linguistics
<Being grateful to the mathematical pioneers>

On language universals, group theory is considered to be hopeful by its conciseness of expression. Especially the way from commutative ring to scheme theory is helpful to resolve the problems a step or two.

Linguistic Premise
2
 Linguistic Note
3
 Linguistic Conjecture
Linguistic Focus
Linguistic Result
 

Distance Theory Algebraically Supplemented

Algebraic Note
Ring
Polydisk <Bridge between Ring and Brane>
Homology Group
Algebraic cycle

Preparatory Consideration
Distance

Space <9th For KARCEVSKIJ Sergej>
Point

Brane Simplified Model
Bend
Distance <Direct Succession of Distance Theory>
S3 and Hoph Map 

Noncommutative Distance Theory

Note
Groupoid
C*-Algebra
Point Space
Atiyah’s Axiomatic System
Kontsevich Invariant

[References]
Conjecture and Result
Sentence versus Word 
Deep Fissure between Word and Sentence


Clifford Algebra



Note
From Super Space to Quantization
Anti-automorphism
Anti-self-dual Form
Dirac Operator
TOMONAGA's Super Multi-time Theory
Periodicity
Creation Operator and Annihilation Operator


Conjecture
Meaning Product 

Kac-Moody Lie Algebra 

Note
Kac-Moody Lie Algebra
Quantum Group

Conjecture
Finiteness in Infinity on Language

Operator Algebra 

Note
Differential Operator and Symbol
Self-adjoint and Symmetry
Frame Operator

Conjecture
Order of Word
Grammar
Recognition

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3.
After writing von Neumann Algebra 1 - 4,  I successively wrote the next.


Functional Analysis 
Reversion Analysis Theory 
Holomorphic Meaning Theory 
Stochastic Meaning Theory

Especially Stochastic Meaning Theory clearly showed me the relationship between mathematics and physics, for example Brownian motion in language. After this theory I really entered the algebraic geometrical writing by Complex manifold deformation Theory. The papers are shown at Zoho site's sekinanlogos.

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Complex Manifold Deformation Theory
  1. Distance of Word
  2. Reflec bsp;of Word 
  3. Uniqueness of Word
  4. Amplitude of Meaning Minimum  
  5. Time of Word
  6. Orbit of Word 
  7. Understandability of Language     

Topological Group Language Theory
  1. Boundary of Words

Symplectic Language
  1. Symplectic Topological Existence Theorem 
  2. Gromov-Witten Invariantational Curve
  3. Mirror Symmetry Conjecture on Rational Curve   ​ 
  4. Isomorphism of Map Sequence  
  5. Homological Mirror Symmetry Conjecture by KONTSEVICH 
  6. Structure of Meaning

Floer Homology Language
  1. Potential of Language       
  2. Supersymmetric Harmonic Oscillator 
  3. Grothendieck Group   ​ 
  4. Reversibility of language
  5. Homology Generation of Language 
  6. Homology Structure of word 
  7. Quantization of Language
  8. Discreteness of Language
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4.
The learning from von Neumann Algebra 1 ended for a while at Floer Homology Language,  where I first got trial papers on language's quantisation or discreteness. The next step was a little apart from von Neumann algebra or one more development of algebra viz. arithmetic geometry.

#
Here ends the paper.
## 
The cited papers' texts are also shown at this site.

Tokyo
3 December 2015
SILnote

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