The Days of von Neumann Algebra 2015

 The Days of von Neumann Algebra

viz.
The cited papers' texts are shown at the blog site SRFL News' January 2015 blogs. 

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 On Infinity of Language1 von Neumann Algebra 12 von Neumann Algebra 23 von Neumann Algebra 34 von Neumann Algebra 4References1 Algebraic Linguistics 2 Distance Theory Algebraically Supplemented3 Noncommutative Distance Theory4 Clifford Algebra5 Kac-Moody Lie Algebra6 Operator Algebra

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2.
The papers of von Neumann Algebra and References are the next. von Neumann Algebra 1 1 Measure2 Tensor Product3 Compact Operator von Neumann Algebra 21 Generation Theorem von Neumann Algebra 31 Properly Infinite2 Purely Infinite von Neumann Algebra 41 Tomita's Fundamental Theorem2 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 Premise2 Linguistic Note3 Linguistic Conjecture4 Linguistic Focus5 Linguistic Result  Distance Theory Algebraically SupplementedAlgebraic Note1 Ring2 Polydisk <Bridge between Ring and Brane>3 Homology Group4 Algebraic cyclePreparatory Consideration1 Distance2 Space <9th For KARCEVSKIJ Sergej>3 PointBrane Simplified Model1 Bend2 Distance <Direct Succession of Distance Theory>3 S3 and Hoph Map  Noncommutative Distance TheoryNote1 Groupoid2 C*-Algebra3 Point Space4 Atiyah’s Axiomatic System5 Kontsevich Invariant[References]Conjecture and Result1 Sentence versus Word 2 Deep Fissure between Word and Sentence Clifford AlgebraNote1 From Super Space to Quantization2 Anti-automorphism3 Anti-self-dual Form4 Dirac Operator5 TOMONAGA's Super Multi-time Theory6 Periodicity7 Creation Operator and Annihilation OperatorConjecture1 Meaning Product  Kac-Moody Lie Algebra Note1 Kac-Moody Lie Algebra2 Quantum GroupConjecture1 Finiteness in Infinity on Language Operator Algebra Note1 Differential Operator and Symbol3 Self-adjoint and Symmetry4 Frame OperatorConjecture1 Order of Word2 Grammar3 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. 

• sekinanlogos

 Complex Manifold Deformation Theory

• Distance of Word
• Reflection of Word 
• Uniqueness of Word
• Amplitude of Meaning Minimum  
• Time of Word
• Orbit of Word 
• Understandability of Language     
• Topological Group Language Theory
• Boundary of Words

 Symplectic Language

• Symplectic Topological Existence Theorem 
• Gromov-Witten Invariantational Curve
• Mirror Symmetry Conjecture on Rational Curve    
• Isomorphism of Map Sequence  
• Homological Mirror Symmetry Conjecture by KONTSEVICH 
• Structure of Meaning

 Floer Homology Language

• Potential of Language       
• Supersymmetric Harmonic Oscillator 
• Grothendieck Group    
• Reversibility of language
• Homology Generation of Language 
• Homology Structure of word 
• Quantization of Language
• Discreteness 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
.## The cited papers' texts are also shown at this site. 

vide:
The days between von Neumann Algebra and Complex Manifold Deformation Theory  

Tokyo
3 December 2015
SIL

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