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Computing $x\cdot e_n \cdot x \cdot e_n$ in a Clifford algebra over $\mathbb{C}^d$

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#linear-algebra #multilinear-algebra #exterior-algebra #clifford-algebras #geometric-algebras
94
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What is the intuition behind the regressive product and its axioms?

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#linear-algebra #abstract-algebra #clifford-algebras #geometric-algebras
34
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Adjoint representation of $V\subset \text{Cl}(V,q)$

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#linear-algebra #clifford-algebras #spin-geometry
45
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Viewing vectors in a Clifford algebra as reflections

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#linear-algebra #multilinear-algebra #exterior-algebra #clifford-algebras #geometric-algebras
36
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Explicit triality representation in Spin(8)

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#group-theory #clifford-algebras #spin-geometry
63
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Why are Dirac spinor representations defined as a projection onto the first factor?

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#differential-geometry #representation-theory #mathematical-physics #clifford-algebras #spin-geometry
98
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What justifies the statement that a Dirac spinor can be written as two Weyl spinors?

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#differential-geometry #representation-theory #mathematical-physics #clifford-algebras #spin-geometry
93
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$R \otimes_k \mathrm{End}_R(W) \cong \mathrm{End}_k(W)$ for a $k$-algebra $R$.

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#abstract-algebra #tensor-products #clifford-algebras
119
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Is the inverse of a $k$-vector a $k$-vector?

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#clifford-algebras #geometric-algebras
50
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Conjugate of an operator and its relation with its squaring value

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#representation-theory #clifford-algebras #hermitian-matrices
28
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Is every element of Spin(4) an element of Spin(8)?

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#group-theory #clifford-algebras
55
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Table of Clifford Algebras

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#solution-verification #vector-bundles #clifford-algebras #k-theory
52
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Uniqueness of the spinor representation

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#abstract-algebra #clifford-algebras
43
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Associated graded algebra of Clifford algebra $\text{Cl}(V,q)$

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#linear-algebra #clifford-algebras #spin-geometry
34
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Polynomial Functions on Matrix Representations of a Clifford Algebra

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#polynomials #taylor-expansion #mathematical-physics #trace #clifford-algebras

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