The Days of von Neumann Algebra

The Days of von Neumann Algebra 

viz. The cited papers' texts are shown at 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 Algebra5 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 Measure2 Tensor Product3 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 Point

Brane 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. 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.

Tokyo

3 December 2015

SILnote