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Why do division algebras always have a number of dimensions which is a power of $2$?

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#binary #quaternions #division-algebras #octonions #sedenions
302
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Brauer group of cyclic extension of the rationals

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#abstract-algebra #field-theory #galois-theory #division-algebras #brauer-group
619
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Show that $\Bbb R^{2n+1}$ is not a division algebra over $\Bbb R$ for $n>0$

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#abstract-algebra #algebraic-topology #algebras #division-algebras
441
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Parallelization of a Sphere gives Division Algebra

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#general-topology #algebraic-topology #geometric-topology #division-algebras
170
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concept of conjugacy class in a ring

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#abstract-algebra #ring-theory #division-algebras
100
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Existence of a division ring on a field.

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#abstract-algebra #extension-field #division-algebras
104
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4-D lattices and quaternions

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#abstract-algebra #quaternions #division-algebras
253
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Quaternion algebra and norm

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#abstract-algebra #division-algebras
653
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Statement equivalent to fundamental theorem of algebra

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#abstract-algebra #field-theory #division-algebras
869
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normed division algebra

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#ring-theory #division-algebras
249
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Is $SL_1(D)$ topologically finitely generated, for $D$ a division algebra over a local field?

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#group-theory #topological-groups #division-algebras #subgroup-growth
2.8k
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Brauer group of a field of rational numbers

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#abstract-algebra #group-theory #field-theory #division-algebras
124
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A corollary to the Wedderburn-Artin theorem.

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#linear-algebra #abstract-algebra #representation-theory #division-algebras
79
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Brauer equivalence classes over $\mathbb{Q}$.

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#abstract-algebra #division-algebras
386
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Schur's Lemma and division algebras

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#linear-algebra #abstract-algebra #group-theory #matrices #division-algebras

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