MathGloss

The quaternion algebra $\mathbb H$ is the four-dimensional associative algebra over $\mathbb R$ spanned by the elements $1,\mathbf i,\mathbf j,\mathbf k$ where $1$ is the identity element and the relations

1. $\mathbf i^2 = \mathbf j^2 = \mathbf k^2 = -1$;
2. $\mathbf{ij} = \mathbf k$;
3. $\mathbf{ji} = -\mathbf k$;
4. $\mathbf{jk} = \mathbf i$;
5. $\mathbf{kj} =-\mathbf i$;
6. $\mathbf{ki} = \mathbf j$;
7. $\mathbf{ik} = -\mathbf j$.

Wikidata ID: Q173853

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