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...

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,...

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...

combinatorics C*-algebra – Topological complex vector space Clifford algebra – Algebra based on a vector space with a quadratic form Commutative algebra – Branch...

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

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

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...

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

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the...

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

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...

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

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

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

division algebra over the real numbers, and therefore a ring, also a division ring and a domain. It is a special case of a Clifford algebra, classified...

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

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...

of f. 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...

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more...

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

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

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...

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

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...

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