# Quantum Matrices

1. Dec 6, 2004

### ^_^

I just started working with mathematical physics coming from a straight physics background. The actual work doesn't seem that hard but some of the notation is unfamilar.

The work is "A Short Course on Quantum Matrices" by Mitsuhiro Takeuchi that can be found at:

http://www.msri.org/publications/books/Book43/files/takeuchi.pdf

Definition 1.5 on p 386 presents the first display of my ignorance...what is M2, M4, what is the circle with the cross and what is the Yang Baxter equation trying to tell me?

Basically what the hell is happening on that whole page from Definition 1.5 onwards? Proposition 1.6 is just as forign to me. Don't warry about things from section 2.

Where can I find a list of all the notation that I should have picked up in an undergrad degree in maths but instead I was off doing physics?

2. Dec 7, 2004

### matt grime

$$\otimes$$ is the tensor product.

M_n(k) is the nxn matrices with entries in the field k

Yang Baxter is telling you how to commute some elements in the algebra, though I forget the analogies people make.

q is an indeterminate, it measures how far way from being the ordinary case the quantum case is. Usually, the limit as q tends to 0 is the classical case.

The notation M_n is undergrad. The tensor product probably isn't in most places.

www.dpmms.cam.ac.uk/~wtg10

on the page of mathematical discussions, there is one called "lose your fear of tensor products".