\ldots ,0,1)} In left quaternionic vector space H n {\displaystyle H^{n}} we use componentwise sum of vectors and product of vector over scalar ( p 1 ,...

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...

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

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,...

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...

sum of real and quaternionic representations is neither real nor quaternionic in general. A representation on a complex vector space can also be isomorphic...