2
votes
1answer
49 views

Number of Involutive Automorphisms on a Clifford Algebra

Let $V$ be a vector space with dimension $n$ and $q$ a quadratic form on $V$. How many involutive automorphisms are there in $\mathcal{Cl}(V,q)$?
1
vote
0answers
228 views

Spinor representation and Clifford modules

Let $V$ be an even-dimensional real inner product space. We denote the Clifford algebra of $V$ by $C(V)$ and the spinor representation by $S$. For a finite-dimensional $\mathbb Z_2$-graded complex ...
4
votes
1answer
102 views

Set of 4 anticommutative matrices

How would you go about showing that there cannot be a set of four 2 by 2 matrices that satisfy the anticommutative relation $AB + BA = 0 $ or $2I$ if $A=B$? i.e minimum order has to be 4. I know that ...
0
votes
1answer
90 views

Hermiticity of a Matrix representing a Clifford alg. element

I'm interested in representations of the elements of a Clifford algebra, $\gamma^a$ with $a\in \{1,...,n\}$, such that $(\gamma^a)^2 =\pm 1$. If these were numbers, for those $\gamma^a=1$ one have ...
3
votes
1answer
322 views

Properties of different matrix representations of clifford algebras

I am looking for some theorems about matrix representations of Clifford algebras. Let $a \in G_{p,q,r}$, where $p$ elements square to $1$, $q$ to $-1$, and $r$ to $0$, that is ...
12
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 ...
4
votes
1answer
121 views

Automorphism groups of real clifford algebras

I'm sure someone has already worked-out what all the relevant groups really are; my question is about how signature duality interacts with these groups. So, by an awful calculation, and choosing a ...