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The Hurwitz quaternions form an order (in the sense of ring theory) in the division ring of quaternions with rational components. It is in fact a maximal order ; this accounts for its importance. The Lipschitz quaternions, which are the more obvious candidate for the idea of an integral quaternion , also form an order.
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 surface theory, in connection with surfaces with maximal symmetry , namely the Hurwitz surfaces . [ 1 ]
The field of complex numbers is also isomorphic to three subsets of quaternions.) [22] A quaternion that equals its vector part is called a vector quaternion. The set of quaternions is a 4-dimensional vector space over the real numbers, with {,,,} as a basis, by the component-wise addition
Adolf Hurwitz (German: [ˈaːdɔlf ˈhʊʁvɪts]; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory. Early life [ edit ]
Hurwitz and Frobenius proved theorems that put limits on hypercomplexity: Hurwitz's theorem says finite-dimensional real composition algebras are the reals , the complexes , the quaternions , and the octonions , and the Frobenius theorem says the only real associative division algebras are , , and .
The ring of Hurwitz quaternions, also known as integral quaternions. A quaternion a = a 0 + a 1 i + a 2 j + a 3 k is integral if either all the coefficients a i are integers or all of them are half-integers. All free associative algebras. [1]
Matthew Perry’s ex-fiancée Molly Hurwitz was seen for the first time since the actor’s death.. Hurwitz, 32, could be seen relaxing in a park with friends in Los Angeles on Sunday, October 29 ...
24 unit Hurwitz quaternions form vertices of a 24-cell and 4 cyclic orbits (grey, blue, purple, orange) of 6 elements each. All 24 elements are depicted (as balls), but only 59 polychoron’s edges of 96 total are visible as straight line segments, and yet 13 show as curved lines and arrows. 24 edges are completely missing, although 2 of them ...