1
vote
0answers
28 views

An algebra associated with an important function

In the paper here the authors make a claim that the Natanzon potential (an implicit potential very important in mathematical physics) follows an $SO(2,2)$ algebra. This potential defined as : $$ ...
1
vote
0answers
19 views

Differential Realizations of certain algebras

I'm a first year graduate student in Mathematical Physics, and I am trying to generalise a certain method involving the so-called "Differential realizations" of certain algebras. The problem I'm ...
0
votes
1answer
40 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
73 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
48 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
77 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 ...
11
votes
3answers
1k 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
40 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
147 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
51 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 ...