division algebra


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division algebra

[də′vizh·ən ‚al·jə·brə]
(mathematics)
A hypercomplex system that is also a skew field.
References in periodicals archive ?
An algebra A in C is said to be a division algebra if any nonzero homogeneous element has a left and a right inverse.
Because the octavian algebra is a division algebra [1,2] then for each octavians u and [u.
Let D be a non-trivial quaternion division algebra over a non-archimedean localization field k.
One potential difficulty with BQM is that the biquaternions are not a division algebra (i.
In 1972, Amitsur discovered the first noncrossed product division algebra ([Am]).
K] ([DELTA]) < [infinity]; we say that [DELTA] is a division algebra over K, for short.
a] : A [right arrow] A, x [right arrow] xa are invertible for all a [member of] A \ {0}, then A is called a division algebra.
Next, we consider the case of the Witt group of a quaternion division algebra endowed with its canonical involution.
The seven chapters in the volume are dedicated to nonlinear elliptic equations, division algebras, exceptional lie groups, and calibrations, Jordan algebras and the Cartan isoparametric cubics, solutions from trialities and isoparametric forms, cubic minimal cones, and singular solutions in calibrated geometrics.
It is known that there exist topological division algebras which are not topologically isomorphic to C (see, for example, [42], pp.
Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted K-theory, noncommutative Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.
This time it was decided to expand the scope by including some further topics related to interpolation, such as inequalities, invariant theory, symmetric spaces, operator algebras, multilinear algebra and division algebras, operator monotonicity and convexity, functional spaces and applications and connections of these topics to nonlinear partial differential equations, geometry, mathematical physics, and economics.

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