In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd...
8 KB (1,242 words) - 12:04, 5 October 2023
Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra (and hence the largest ring). Further extending the quaternions yields...
96 KB (12,654 words) - 08:09, 19 July 2024
The set of Hurwitz quaternions forms a ring; that is to say, the sum or product of any two Hurwitz quaternions is likewise a Hurwitz quaternion. The (arithmetic...
25 KB (4,264 words) - 15:18, 17 July 2024
The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann...
6 KB (808 words) - 09:12, 30 January 2024
Hurwitz matrix Hurwitz numbers Hurwitz polynomial Hurwitz problem Hurwitz quaternion order Hurwitz quaternion Hurwitz scheme Hurwitz surface Hurwitz zeta...
9 KB (985 words) - 09:44, 20 August 2024
In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...
10 KB (1,532 words) - 15:42, 21 February 2024
Versor (redirect from Unit quaternion)
include the twenty-four Hurwitz quaternions that have the norm 1 and form vertices of a 24-cell polychoron. Hamilton defined a quaternion as the quotient of...
19 KB (2,804 words) - 22:37, 12 July 2024
In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...
26 KB (3,724 words) - 08:50, 20 June 2024
E(α) of conjugation α(⋅)α by the Hurwitz quaternion α = m + ni + pj + qk restricted to the subspace of quaternions spanned by i, j, k, which is given...
10 KB (1,377 words) - 22:22, 22 June 2024
(2,3,7) triangle group (section Quaternion algebra)
ij = −ji. One chooses a suitable Hurwitz quaternion order Q H u r {\displaystyle {\mathcal {Q}}_{\mathrm {Hur} }} in the quaternion algebra. Here the order Q...
6 KB (818 words) - 07:56, 28 October 2023