Saturday, January 19, 2019

A canonical Musical Isomorphism (but not Isospectral) - the math-music noncommutative secret to martial arts nonwestern alchemy unified field Reality





It's fun to discover this MUSIC theory equation - embedded into unified field noncommutative math - this originates from Alain Connes Watch/Listen to Connes' new music math vid! music analysis. https://mathoverflow.net/questions/69074/the-origin-of-the-musical-isomorphisms  Marcel Berger says he does not remember...


Spectral Geometry



by B Iochum - ‎2011 - ‎Cited by 5 - ‎Related articles
Noncommutative geometry, mainly pioneered by A. Connes (see [25,31]), is based on ...... x M (or ClTxM using the musical isomorphism X ∈ TM ↔ X♭ ∈ T∗M).

by A Connes - ‎Cited by 326 - ‎Related articles
A. Connes. Sel. math. ..... The abelian locally compact group Ck is (noncanonically) isomorphic to K ×N. where ... We choose (noncanonically) an isomorphism ...... the obvious existence of signals (a recorded music piece for instance) which for.

So it is now "spread" into noncommutative math simply is the phrase:
a canonical (musical) isomorphism
 

Wiki says they don't know the origin of the term? C'mon! Alain Connes!
In mathematics, the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle and the cotangent bundle of a pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on symplectic manifolds. The term musical refers to the use of the symbols (flat) and (sharp).[1][2] The exact origin of this notation is not known, but the term musicality in this context would be due to Marcel Berger[3].
In covariant and contravariant notation, it is also known as raising and lowering indices.

 

 

by A Ghorbanpour - ‎2015 - ‎Related articles
The Curvature of the Determinant Line Bundle on the Noncommutative Two Torus, ...... For T > 0, the Berger 3-sphere S3(T), introduced by Marcel Berger [3], is a ... where ♭ is the musical isomorphism with respect to the standard round.

 

Spacetimes in Noncommutative Geometry: a definition ... - IOPscience


by F Besnard - ‎2018 - ‎Related articles
theorem, any commutative C∗-algebra A is canonically isomorphic to the algebra of .... 1-forms on M with sections of the Clifford bundle, through the musical.

by F Besnard - ‎2016 - ‎Cited by 10 - ‎Related articles
Mar 13, 2017 - Noncommutative geometry, as initiated by Alain Connes, is an ...... ideal in Cl(V ), be a Clifford-module isomorphism, which we know exists by ...... tion of the musical isomorphism defined by g, and the representation ρ (hence.

by M Lachièze-Rey - ‎2005 - ‎Cited by 13 - ‎Related articles
Jul 13, 2010 - It has a (non commutative) algebra structure with respect to the tensor ... a canonical (musical) isomorphism between V and its dual V ∗, which ...

Mar 9, 2017 - First, note that there are many manifestations of the hyperfinite I I 1 factor, but it turns out that they are all isomorphic. I will thus interpret your ...

Oct 30, 2012 - The title of this post, the music of spheres, refers to a talk The music of shapes which I gave in Lille, on the 26th of September, on the occasion ...
Missing: cliffordisomorph


7.1 Crossed products, the T-C isomorphism and the P-V sequence . 109. 7.1.1 Crossed .... CONTENTS. 1. Clifford algebras and spinor representations. 250. 1.1.

by RO Buachalla - ‎2006 - ‎Related articles
4.1.1 Clifford Algebras . . . . . . . . . . . . . . . . . . . . . . . . 83 .... terpret all of this work as a noncommutative version of differential geometry was a French ..... On the other hand, let Φ be an algebra ∗-isomorphism from A to itself, and consider the ...... The maps, known as the flat, and sharp, musical isomorphisms respectively, are.



No comments:

Post a Comment