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...

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

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...

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

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...

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

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

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

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,...

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, a Lie algebra has been generalized in several ways. A graded Lie algebra is a Lie algebra with grading. When the grading is Z / 2 {\displaystyle...

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

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

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...

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

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

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

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...

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

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

subspace of some Clifford algebra. Witt vector, an infinite sequence of elements of a commutative ring, which belongs to an algebra over this ring, and...

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...

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...

Business Media. ISBN 978-0-7923-2143-9. Alfred Hoblitzelle Clifford; G. B. Preston (1967). The Algebraic Theory of Semigroups. Volume II. American Mathematical...

The Eilenberg–Niven theorem is a theorem that generalizes the fundamental theorem of algebra to quaternionic polynomials, that is, polynomials with quaternion...