complexified algebra
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List of simple Lie groups — In mathematics, the simple Lie groups were classified by Élie Cartan.The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. See also the table of Lie groups for a smaller list of… … Wikipedia
Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… … Wikipedia
Lorentz invariance in loop quantum gravity — Loop quantum gravity (LQG) is a quantization of a classical Lagrangian field theory. It is equivalent to the usual Einstein Cartan theory in that it leads to the same equations of motion describing general relativity with torsion. As such, it can … Wikipedia
Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… … Wikipedia
Hyperbolic quaternion — In mathematics, a hyperbolic quaternion is a mathematical concept first suggested by Alexander MacFarlane in 1891 in a speech to the American Association for the Advancement of Science. The idea was criticized for its failure to conform to… … Wikipedia
Almost complex manifold — In mathematics, an almost complex manifold is a smooth manifold equipped with smooth linear complex structure on each tangent space. The existence of this structure is a necessary, but not sufficient, condition for a manifold to be a complex… … Wikipedia
Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… … Wikipedia
Generalized complex structure — In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures… … Wikipedia
Biquaternion — In abstract algebra, the biquaternions are the numbers where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of… … Wikipedia
Hypercomplex number — The term hypercomplex number has been used in mathematics for the elements of algebras that extend or go beyond complex number arithmetic.Hypercomplex numbers have had a long lineage of devotees including Hermann Hankel, Georg Frobenius, Eduard… … Wikipedia
Simple Lie group — Lie groups … Wikipedia
