mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional...

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

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,...

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...

mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field...

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...

distillation and for quantum error correction. Magic state distillation Clifford algebra Clifford gates Nielsen, Michael A.; Chuang, Isaac L. (2010-12-09). Quantum...

is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring...

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

directed by Paul Flaherty Clifford (Muppet) Clifford algebra, a type of associative algebra, named after William Kingdon Clifford Clifford analysis, a mathematical...

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...

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

Clifford algebra used as forms in Geometric Algebra rather than matrices. Recognising the geometric operations, such as rotations, allows the 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...

relations that ensure they generate a matrix representation of the Clifford algebra   C l 1 , 3 ( R )   . {\displaystyle \ \mathrm {Cl} _{1,3}(\mathbb...

can be constructed as a subgroup of the invertible elements in the Clifford algebra Cl(n). A distinct article discusses the spin representations. The spin...

gauge from the complex Clifford algebra C ℓ 6 {\displaystyle \mathbb {C} \ell _{6}} ", Advances in Applied Clifford Algebras, 28: 52, arXiv:1702.04336...

{\displaystyle Z} -angle rotations are known. Magic state distillation Clifford algebra Gottesman, Daniel (1998-01-01). "Theory of fault-tolerant quantum computation"...

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

like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Composition algebra Differential algebra Free algebra Geometric...

In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a...

Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with...

category Symplectic Clifford algebra, see Weyl algebra Symplectic geometry Symplectic group, and corresponding symplectic Lie algebra Symplectic integrator...

Since the quaternions can be identified as the even subalgebra of the Clifford Algebra Cl(3), SU(2) is in fact identical to one of the symmetry groups of...

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, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) to physics. Spacetime algebra provides...

special unitary group SU(2). The algebra generated by the three matrices σ1, σ2, σ3 is isomorphic to the Clifford algebra of R 3 , {\displaystyle \mathbb...

interest in the theory of solitons and integrable systems. In the Clifford algebra C ℓ ( 2 ) {\displaystyle C\ell (2)} , the complex number z = x + i...