The Days of von Neumann Algebra 2015

The Days of von Neumann Algebra

​The cited papers' texts are shown at Blogger site, SRFL News.

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

• References

1 Algebraic Linguistics
2 Distance Theory Algebraically Supplemented
3 Noncommutative Distance Theory
4 Clifford Algebra
5 Kac-Moody Lie Algebra
6 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 1 Measure
2 Tensor Product
3 Compact Operator

• von Neumann Algebra 2

1 Generation Theorem

• von Neumann Algebra 3

1 Properly Infinite
2 Purely Infinite

• von Neumann Algebra 4

1  Tomita's Fundamental Theorem
2 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.
1 Linguistic Premise
2 Linguistic Note
3 Linguistic Conjecture
4 Linguistic Focus
5 Linguistic Result 

• Distance Theory Algebraically Supplemented

Algebraic Note
1 Ring
2 Polydisk <Bridge between Ring and Brane>
3 Homology Group
4 Algebraic cycle
Preparatory Consideration
1 Distance
2 Space <9th For KARCEVSKIJ Sergej>
3 PointBrane
Simplified Model
1 Bend
2 Distance <Direct Succession of Distance Theory>
3 S3 and Hoph Map 

• Noncommutative Distance Theory

Note
1 Groupoid
2 C*-Algebra
3 Point Space
4 Atiyah’s Axiomatic System
5 Kontsevich Invariant[References]
Conjecture and Result
1 Sentence versus Word
2 Deep Fissure between Word and Sentence

• Clifford Algebra

Note
1 From Super Space to Quantization
2 Anti-automorphism
3 Anti-self-dual Form
4 Dirac Operator
5 TOMONAGA's Super Multi-time Theory
6 Periodicity
7 Creation Operator and Annihilation Operator
Conjecture
1 Meaning Product 

• Kac-Moody Lie Algebra 

Note
1 Kac-Moody Lie Algebra
2 Quantum Group
Conjecture
1 Finiteness in Infinity on Language

• Operator Algebra 

Note
1 Differential Operator and Symbol
3 Self-adjoint and Symmetry
4 Frame Operator
Conjecture
1 Order of Word
2 Grammar
3 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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• sekinanlogos

• Complex Manifold Deformation Theory

1. Distance of Word
2. Reflection 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 Theory

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

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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.

Tokyo
3 December 2015
Sekinan Essay