In mathematics, a generalized Clifford algebra (GCA) is a unital associative algebra that generalizes the Clifford algebra, and goes back to the work of...

As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

Greenbrier Christian Academy, in Chesapeake, Virginia GCA (gene) Generalized Clifford algebra Geochimica et Cosmochimica Acta, a scientific journal Giant-cell...

spin group and its Lie algebra are embedded inside the Clifford algebra in a natural way, and in applications the Clifford algebra is often the easiest...

length. The algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit. Clifford bundle is...

commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation...

be a Clifford algebra over the reals—i.e. coefficients of elements of the algebra are to be real numbers. These algebras, called geometric algebras, form...

quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices...

spinors (or simple spinors) are spinors that are annihilated, under the Clifford algebra representation, by a maximal isotropic subspace of a vector space V...

Clifford algebra is algebra isomorphic to a full matrix ring over R, C, or H (the quaternions), or to a direct sum of two copies of such an algebra,...

by Lee (1948) and Chevalley (1954) using Clifford algebras. Hurwitz's theorem has been applied in algebraic topology to problems on vector fields on spheres...

Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis...

Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp...

algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras. The tensor algebra also has two coalgebra structures;...

In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...

the Clifford algebra, which is also referred to as the orthogonal Clifford algebra. The Weyl algebra is also referred to as the symplectic Clifford algebra...

kind Jacobian variety Generalized Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's theorem on special divisors...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

orthoschemes - right simplexes (right triangles generalized to n dimensions) - studied by Schoute who called the generalized trigonometry of n Euclidean dimensions...

{\displaystyle q_{ij}\in \mathbb {C} } Any Clifford algebra can be described explicitly using an algebra presentation: given an F {\displaystyle \mathbb...

Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both...

exact. All the above cases may be unified and generalized in universal algebra. Let A and B be algebraic structures of a given type and let f be a homomorphism...

multilinear algebra, such as the tensor algebra, symmetric algebra, and exterior algebra over a given vector space. Graded algebras can be generalized to filtered...

[citation needed] The Weyl algebra An Azumaya algebra The Clifford algebras, which are useful in geometry and physics. Incidence algebras of locally finite partially...

powers of the cotangent bundle. Generalized geometry unites these two fields by treating sections of the generalized tangent bundle, which is the direct...

Bra–ket notation Multilinear subspace learning Multivector Geometric algebra Clifford algebra Closed and exact differential forms Component-free treatment of...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

equals the right hand side. This result can be generalized to higher dimensions using geometric algebra. In particular in any dimension bivectors can be...

geometric algebra, pseudovectors are the elements of the algebra with dimension n − 1, written ⋀n−1Rn. The label "pseudo-" can be further generalized to pseudoscalars...