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The Days of von Neumann Algebra

 

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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.

..............................................................................................................................

• 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.


.................................................................................................................................

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

..................................................................................................................................

• 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
....................................................................................................................................


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.

....................................................................................................................................

• 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

.....................................................................................................................................

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

Thanks to physics about which I ever dreamt in my future

 Thanks to physics about which I ever dreamt in my future

TANAKA Akio

In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse wideness at the university, from where returning the clear descriptive situation represented by physics needed long and winding road for me. Now in my mind probably language and physics or mathematics are happily live together constructing the world's one main frame. I wonder why I took so much time to reach here. Long time ago, at least Pascal's days, philosophy and mathematics were both sides of shield for solving the world's hard problems. It is very appropriate that the fact is solved from every fields not being partitioned any artificial walls. Philosophy may be solved by mathematics and mathematics may opened by physical phenomenon. Now they all became common sense. Only I reached here delaying rather late. I am now situated in tranquil field. Thanks to so many pioneers, especially in mathematics. Also to physics about which I ever dreamt in my future.

References:

1. Substantiality Dedicated to SAPIR Edward / 27 February 2005
2. To my dear friend, KANEKO Yutaka / 22 May 2013
3. Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013 
4. Language, Amalgamation of Mathematics and Physics / 15 April 2014
5. Perhaps Return to Physics /16 August 2014
6. Winding road to physics / 10 April 2015

Tokyo
25 July 2015 Reprint
Sekinan Study

TANAKA Akio

In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse wideness at the university, from where returning the clear descriptive situation represented by physics needed long and winding road for me. Now in my mind probably language and physics or mathematics are happily live together constructing the world's one main frame. I wonder why I took so much time to reach here. Long time ago, at least Pascal's days, philosophy and mathematics were both sides of shield for solving the world's hard problems. It is very appropriate that the fact is solved from every fields not being partitioned any artificial walls. Philosophy may be solved by mathematics and mathematics may opened by physical phenomenon. Now they all became common sense. Only I reached here delaying rather late. I am now situated in tranquil field. Thanks to so many pioneers, especially in mathematics. Also to physics about which I ever dreamt in my future.

References:

1. Substantiality Dedicated to SAPIR Edward / 27 February 2005
2. To my dear friend, KANEKO Yutaka / 22 May 2013
3. Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013 
4. Language, Amalgamation of Mathematics and Physics / 15 April 2014
5. Perhaps Return to Physics /16 August 2014
6. Winding road to physics / 10 April 2015

Tokyo
25 July 2015 Reprint
Sekinan Study