Quaternion Algebra

Mathematics, Central Simple Algebra, Real Number, Quaternion, Quadratic Form, Number Theory, Hilbert Symbol, Local Class Field Theory, Algebra Homomorphism
Erscheinungsjahr 2010
ISBN: 978-613-0-34367-5
Verlag: VDM Verlag Dr. Müller e.K.

Buch, Englisch, 120 Seiten, Paperback, Format (B × H): 150 mm x 220 mm, Gewicht: 197 g

High Quality Content by WIKIPEDIA articles! In mathematics, a quaternion algebra over a field F is a central simple algebra A over F[1][2] that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, A otimes_F K is isomorphic to the 2×2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of the Hamilton quaternions to an arbitrary base field. The Hamilton quaternions are a quaternion algebra (in the above sense) over F = mathbb{R} (the real number field), and indeed the only one over R apart from the 2×2 real matrix algebra, up to isomorphism.

Autoren/Hrsg.

Surhone, Lambert M.

Timpledon, Miriam T.

Marseken, Susan F.