split algebra
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Split-complex number — A portion of the split complex number plane showing subsets with modulus zero (red), one (blue), and minus one (green). In abstract algebra, the split complex numbers (or hyperbolic numbers) are a two dimensional commutative algebra over the real … Wikipedia
Split-biquaternion — In mathematics, a split biquaternion is a hypercomplex number of the form where w, x, y, and z are split complex numbers and i, j, and k multiply as in the quaternion group. Since each coefficient w, x, y, z spans two real dimensions, the split… … Wikipedia
Split-quaternion — Coquaternion multiplication × 1 i j k 1 1 i j k i i −1 k −j j j −k +1 −i … Wikipedia
Split-octonion — In mathematics, the split octonions are a nonassociative extension of the quaternions (or the split quaternions). They differ from the octonions in the signature of quadratic form: the split octonions have a split signature (4,4) whereas the… … Wikipedia
Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… … Wikipedia
Compact Lie algebra — Lie groups … Wikipedia
Octonion algebra — In mathematics, an octonion algebra over a field F is an algebraic structure which is an 8 dimensional composition algebra over F. In other words, it is a unital nonassociative algebra A over F with a nondegenerate quadratic form N (called the… … Wikipedia
Relational algebra — Not to be confused with Relation algebra. Relational algebra, an offshoot of first order logic (and of algebra of sets), deals with a set of finitary relations (see also relation (database)) that is closed under certain operators. These operators … Wikipedia
Normed division algebra — In mathematics, a normed division algebra A is a division algebra over the real or complex numbers which is also a normed vector space, with norm || · || satisfying the following property: for all x and y in A. While the definition allows normed… … Wikipedia
Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… … Wikipedia
Nilradical of a Lie algebra — In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical of a finite dimensional Lie algebra is its maximal nilpotent ideal, which exists because the sum of any two nilpotent ideals is… … Wikipedia
