What is Connes fusion and its connection to commutivity?

[MathematicalPhysicist]

can someone explain to me this term?
i know that's it is concenered to commutivity (or the lack of it).

 

[HallsofIvy]

I am afraid you will have to give us more information on where you saw or hear of "connes fusion". I've never seen the term before!

 

[Lonewolf]

I think it's some kind of tensor product between quantum groups. This is off the top of my head from a book I picked up about six months ago, so it's more than likely inaccurate...

 

[marcus]

Originally posted by Lonewolf
I think it's some kind of tensor product between quantum groups. This is off the top of my head from a book I picked up about six months ago, so it's more than likely inaccurate...

That's not so inaccurate! I think the first use of the term
"Connes fusion" was in a 1998 paper by Tony Wassermann at Cambridge

http://arxiv.org/abs/math.OA/9806031

and he references the 1994 book by Alain Connes "Non-commutative Geometry"

A group representation can be thought of as a 'module' and there is a way to "fuse" two representations together which is essentially taking a kind of "tensor product" of two modules.
And Connes talked about ways of fusing or multiplying together two modules.

Then in 1998 Anthony Wassermann was writing about Algebraic Quantum Field Theory and fusing two representations and he introduced the idea of "Connes fusion" in the first paragraph of the paper.

too bad its just a fusion of two algebraic structures and not some kind of new source of energy that would replace the need for petroleum