A set of valuable universal similarity factorization equalities are established over complex Clifford algebras Cn. Through them matrix representations of complex Clifford algebras Cn can directly be derived, and their properties can easily be determined. AMS Subject Classification: 15A23, 15A66.

This paper is concerned with the modular representation theory of the affine Hecke-Clifford superalgebra, the cyclotomic Hecke-Clifford superalgebras, and projective representations of the symmetric group. Our approach exploits crystal graphs of affine Kac-Moody algebras.

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles ( bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D4−D5−E6−E7−E8 model of Smith based on the underlying Clifford algebraic structures in D = 8...

We consider a straightforward extension of the 4-dimensional spacetime M4 to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in M4. All those objects can be elegantly represented by the Clifford numbers X ≡ xγA ≡ x γa1...ar , r = 0, 1, 2, 3, 4. This leads to the concept of the so-called Clifford space C, a 16-dimension...

We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Cliff...

Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined presentation of Matsumoto and Amano’s results, simplifying some proofs along the way. We also point out some corollaries to Matsumoto and Amano’s work, includ...

After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl 2m that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last part we apply these results to the Clifford algebra formulation of the NP-complete problem of the m...

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4, 0), this parametrizat...