Research Topics in Algebraic Foundations of Quantum Algebraic Topology

topic on the Algebraic Foundations of Quantum Algebraic Topology

topic on the Algebraic Foundations of Quantum Algebraic Topology

topic on the Algebraic Foundations of Quantum Algebraic Topology

This is a contributed topic on the

algebraic

foundations

of Quantum

Algebraic Topology

(QAT)

(A.)

Quantum Algebraic Topology (QAT)

is defined as the mathematical and physical study of general theories of quantum

algebraic structures

from the standpoint of Algebraic Topology,

Category Theory

and their

Non-Abelian

extensions

in

Higher Dimensional Algebra

and

Supercategories

in

relation

to, or petinent to,

Quantum theories

,

Quantum Field Theories

,
General Relativity and its Quantum extensions,

Quantum Gravity

.

(B). Several suggested new QAT topics are:

(1)

Poisson algebras

,

Quantization

methods and Hamiltonian algebroids

(2)

K-S

Theorem

and its Quantum algebraic

consequences

in QAT

(3)

Logic Lattice algebras or Many-Valued (MV)

Logic algebras

(4)

Quantum MV-Logic

algebras

and

Ł

-

M

n

-noncommutative algebras

(5)

Quantum Operator Algebras

( such as :

involution

, *-algebras, or

*

-algebras,

von Neumann algebras

, JB- and JL- algebras,

C

*

- or C*- algebras, etc.

(6)

Quantum von Neumann algebra and subfactors

(7)

Kac-Moody and K-algebras

(8)

Hopf algebras

,

Quantum Groups

and Quantum group algebras

(9)

Quantum Groupoids

and weak Hopf

C

*

-algebras

(10)

Groupoid

C*-

Convolution algebras

and *-Convolution Algebroids

(11)

Quantum Spacetimes and

Quantum Fundamental Groupoids

(12)

Quantum Double

Algebras

(13)

Quantum Gravity,

supersymmetries

, supergravity,

superalgebras

and graded ‘Lie’ algebras

(14)

Quantum

Categorical algebra

and Higher Dimensional,

Ł

-

M

n

- Toposes

(15)

Quantum

R-categories

, R-supercategories and Symmetry Breaking

(16)

Extended Quantum Symmetries in Higher Dimensional Algebras (HDA), such as:

algebroids, double algebroids,

categorical

algebroids,

double groupoids

,

convolution algebroids, groupoid

C

*

-convolution algebroids

(17)

Universal algebras

in R-Supercategories

(18)

Supercategorical algebras (SA) as concrete

interpretations

of the Theory of

Elementary

Abstract Supercategories (ETAS).

(19)

Quantum Non-Abelian Algebraic Topology (QNAAT)

(20)

Noncommutative Geometry

,

Quantum Geometry

, and Non-Abelian Quantum

Algebraic Geometry

(21)

Other – Miscellaneous

[please add here your

additions

, changes, editing,
remarks, proofs, conjectures, and so on…]

References

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Abstract and Preprint of Report

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17

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Title

topic on the Algebraic Foundations of Quantum Algebraic Topology

Canonical name

TopicOnTheAlgebraicFoundationsOfQuantumAlgebraicTopology12

Date of creation

2013-03-11 19:51:44

Last modified on

2013-03-11 19:51:44

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