**The Days of von Neumann Algebra**

**viz.**

**The cited papers' texts are also shown at this site.**

**TANAKA Akio**

**1.**

My

**s**tudy'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 Algebra5 Kac-Moody Lie Algebra

6 Operator Algebra

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

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

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.

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

Complex Manifold Deformation Theory

Topological Group Language Theory

Symplectic Language

Floer Homology Language

4.

The learning from von Neumann Algebra 1 ended for a while

Functional Analysis

Reversion Analysis Theory

Holomorphic Meaning Theory

Stochastic Meaning Theory

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.

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

Complex Manifold Deformation Theory

Topological Group Language Theory

Symplectic Language

Floer Homology 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.

**Tokyo**

**3 December 2015**

**SILnote**

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