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**Quaternionic representation**— In mathematical field of representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure, i.e., an antilinear equivariant map:jcolon V o V, which satisfies:j^2=… … Wikipedia**Quaternionic projective space**— In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is… … Wikipedia**Quaternionic vector space**— A left (or right) quaternionic vector space is a left (or right) H module where H denotes the noncommutative ring of the quaternions.The space H n of n tuples of quaternions is both a left and right H module using the componentwise left and right … Wikipedia**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**Hyperkähler manifold**— In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4 k and holonomy group contained in Sp( k ) (here Sp( k ) denotes a compact form of a symplectic group, identifiedwith the group of quaternionic linear unitary … 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**Symplectic group**— For finite groups with all characteristc abelian subgroups cyclic, see group of symplectic type. Group theory … Wikipedia**Real representation**— In the mathematical field of representation theory a real representation is usually a representation on a real vector space U , but it can also mean a representation on a complex vector space V with an invariant real structure, i.e., an… … Wikipedia**Bott periodicity theorem**— In mathematics, the Bott periodicity theorem is a result from homotopy theory discovered by Raoul Bott during the latter part of the 1950s, which proved to be of foundational significance for much further research, in particular in K theory of… … Wikipedia**Quaternion-Kähler manifold**— In differential geometry, a quaternion Kähler manifold (or quaternionic Kähler manifold) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp( n )·Sp(1). Another, more explicit, definition, uses a 3 dimensional subbundle H … Wikipedia