# Tagged Questions

Clifford algebras are associative algebras constructed from quadratic forms on vector spaces. They can be viewed as generalizations of the real numbers, complex numbers, and quaternions. These algebras have applications in geometry and theoretical physics.

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### Good introductory book on geometric algebra

The title of the question already says it all but I would like to add that I would really like the book to be more about geometric algebra than its applications : it should contain theorems' proofs. ...
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### Are Clifford algebras and differential forms equivalent frameworks for differential geometry?

I recently discovered Clifford's geometric algebra and its application to differential geometry. Some claim that this conceptual framework subsumes and generalizes the more traditional approach based ...
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### 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 is?...
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### How do you show that the Laplacian is the square of the (Euclidean) Dirac operator?

If I understand correctly, the Euclidean Dirac operator is given by $$D=\sum_{i=1}^n e_i \frac{\partial}{\partial x_i},$$ where $e_i$ are bases for $Cl_{0,n}(\mathbb{R})$, i.e., the $n$-dimensional ...
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### Why is the radical of a Clifford algebra generated by the kernel of the associated symmetric form? [duplicate]

I was recently reading through Jacobson's Basic Algebra. I got to the section on Clifford algebras, and have the following question. Let $Cl_\omega$ be the Clifford algebra with bilinear symmetric ...
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### Looking for a clear definition of the geometric product

In brief: I'm looking for a clearly-worded definition1 of the geometric product of two arbitrary multivectors in $\mathbb{G}^n$. I'm having a hard time getting my bearings in the world of "...
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### The pushforward under the left action in the group of units of a Clifford algebra

The following I know to be true: let $A$ and $B$ be elements of $GL(m,\mathbb{R})$ and let $X \in T_BGl(m, \mathbb{R})$ and let $L_A:Gl(m, \mathbb{R}) \to GL(m, \mathbb{R})$ be the left multiplication ...
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### 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 ...