In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained complex matrices corresponding to basis of quaternions. Also, investigated features matrices. get Pauli Then, have shown that produced these is isomorphic Clifford Cl(E_αβ^3) space E_αβ^3.
 Finally, studied relations among symplecti...

In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to ...

Mathias Soeken, D. Michael Miller, and Rolf Drechsler Institute of Computer Science, University of Bremen, Germany Department of Computer Science, University of Victoria, BC, Canada The Pauli matrices are a set of three 2×2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are...

Considered is the multiplicative semigroup of ratios of products of principal minors bounded over all positive definite matrices. A long history of literature identifies various elements of this semigroup, all of which lie in a subsemigroup generated by Hadamard-Fischer inequalities. Via cone-theoretic techniques and the patterns of nullity among positive semidefinite matrices, a semigroup cont...

We prove refined enumeration results on several symmetry classes as well related of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model statistical physics. More precisely, we study vertically symmetric, and horizontally perverse, off-diagonally off-antidiagonally quarter turn symmetric quasi matrices. Our conjectures Fischer, Duchon Robbins.

In this paper we study the quantum Clifford-Hopf algebras ̂ CHq(D) for even dimensions D and obtain their intertwiner R−matrices, which are elliptic solutions to the Yang-Baxter equation. In the trigonometric limit of these new algebras we find the possibility to connect with extended supersymmetry. We also analyze the corresponding spin chain hamiltonian, which leads to Suzuki’s generalized XY ...

In this paper, we derive a canonical representation for the first order hyperbolic equation systems with their coefficient matrices satisfying the Clifford algebra Cl(1, 3), and then demonstrate some of its applications. This canonical formalism can naturally give a unified description for the fundamental fields in physics. PACS numbers: 11.10.-z, 11.10.Cd, 12.10.-g

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize standard (pseudo)-Riemannian metric Dirac matrices. show for flat metrics there is triangle map constructed from [Formula: see text]-forms on text], extension relevant operators.