4
votes
2answers
93 views

Identifying the algebra

In order to solve an obscure (physics) problem I have been considering whose details are not important, I am looking for elements (I am thinking in terms of matrices and their products but this may ...
0
votes
1answer
68 views

Finding Percentage Contribution of a Variable in an Equation

I have an equation, for example: $$ y=a-b+c $$ I am actually confused how exactly to find the contribution of the variables individually to the entire equation. Due to the negative sign, following ...
2
votes
0answers
77 views

Status of a question from Freeman Dyson's 1972 article

In a famous article, Freeman Dyson mentions an interesting relationship between the $\tau$ functions of number theory and the dimensions of finite-dimensional simple Lie algebras (section 2). He ...
1
vote
0answers
57 views

An $SU(3)$ isomorph in Clifford $G(5,0)$?

I am a computer scientist using the geometric (Clifford) algebras $G(n,0)$ over $\mathbb{Z}_3 = \{0,1,-1\}$ to describe distributed computations. My question concerns $G(5,0)$ with generators ...
1
vote
1answer
79 views

What are the structure constants for the algebra of quaternions? Show this algebra is associative.

What are the structure constants for the algebra of quaternions? Show this algebra is associative. How can I find the structure constants? I know that for an algebra $\mathscr{A}$ and basis ...
12
votes
3answers
2k views

What's the Clifford algebra?

I'm reading a book on Clifford algebra for physicists. I don't quite understand it conceptually even if I can do most algebraic manipulations. Can some-one teach me what the Clifford algebra really ...
2
votes
1answer
41 views

Tensoring Spectral triples that are composed from Real algebras.

I have a misunderstanding that I am hoping is really quite trivial. In connes standard Non-commutative geometry model of electroweak interactions he takes the algebra input in his finite spectral ...
2
votes
1answer
157 views

Invariant polynomials

Let $A\in Mat_{2}(2\times2;\mathbb{R})$and consider the action of the 1-parameter group $e^{tA}$ on $\mathbb{R}^{2}$. Describe all 1-parameter groups etA which have a nonconstant invariant polynomial. ...
0
votes
1answer
55 views

Quotient map-torus

Let $e_{1},e_{2}$ be a frame of $\mathbb{R}^{2}$. $G=(ne_{1}+me_{2} : n,m \in \mathbb{Z})$ be a subgroup acting on $\mathbb{R}^{2}$ by translation.Show that the quotient map $\pi ...