In mathematics, a left (or right) quaternionic vector space is a left (or right) H {\displaystyle \mathbb {H} } -module where H {\displaystyle \mathbb...

representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure, i.e., an antilinear...

\bigwedge ^{2k}T^{*}M=\bigwedge ^{4n-2k}T^{*}M.} If we regard the quaternionic vector space H n ≅ R 4 n {\displaystyle \mathbb {H} ^{n}\cong \mathbb {R} ^{4n}}...

summand acting like the unit quaternions on a quaternionic vector space. Thus the quaternion-Kähler symmetric spaces are easily read off from the classification...

Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b...

complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight...

projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension...

g,I,J,K)} is a hyperkähler manifold, then the tangent space TxM is a quaternionic vector space for each point x of M, i.e. it is isomorphic to H n {\displaystyle...

vector space over the field F which preserve a non-degenerate skew-symmetric bilinear form. Such a vector space is called a symplectic vector space,...

skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four...