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...tive algebra]] over a field $F$ that generalises the construction of the [[quaternion]]s over the field of real numbers. The quaternion algebra $(a,b)_F$ is the four-dimensional vector space over $F$with basis $\mathbf{

...Lie algebras over a field of non-zero characteristic see [[Lie algebra|Lie algebra]]). The fact that a finite-dimensional Lie algebra $ \mathfrak g $ is semi-simple is equivalent to any of the following con

...a]]. Each non-zero class contains, up to isomorphism, exactly one division algebra over $k$ (i.e. a skew-field over $k$). ...oup of order two and its non-zero element is the class of the algebra of [[quaternion]]s. If $k$ is the field of $p$-adic numbers or any locally compact field th

...ion algebra (cf. also [[Quaternion|Quaternion]]) over $K$ with exactly one split place at infinity (when $K$ is of odd degree, or when $E$ has at least one