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...

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

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...

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...

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

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

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...

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 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,...

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

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

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

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

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

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

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

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

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...

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

whose Sylow 2-subgroups are generalized quaternion cannot be simple. Another terminology reserves the name "generalized quaternion group" for a dicyclic...

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

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...

multiplication in an R-algebra must be R-bilinear). This R-algebra is denoted R⟨X1,...,Xn⟩. This construction can easily be generalized to an arbitrary set...

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

product, vector calculus does not generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product,...

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...

and for his work on algebraic descriptions of quantum mechanics in terms of underlying symplectic and orthogonal Clifford algebras. Hiley co-authored the...