Results 51 to 60 of about 266 (166)
ScienceOpen Research, 2014 The projective representation of groups was introduced in 1904 by Issai Schur. It differs from the normal representation of groups by a twisting factor, which we call Schur function in this book and which is called sometimes normalized factor set in the ...
Corneliu Constantinescu
doaj +1 more source
A Note on the Representation of Clifford Algebras
Journal of Geometry and Symmetry in Physics, 2020 In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to
openaire +2 more sources
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group $W$ and two skew-polynomial subalgebras of anticommuting generators.
Ta Khongsap, Weiqiang Wang
doaj +1 more source
Clifford Algebras and Possible Kinematics
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all ...
Alan S. McRae
doaj
Representation of Integral Formulas for the Extended Quaternions on Clifford Analysis
MathematicsThis work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu formulas are
Ji Eun Kim
doaj +1 more source
Structure of factor algebras and clifford algebra
Linear Algebra and its Applications, 1996 This paper is concerned with the generalized spectral decomposition or eigenprojector form of a linear operator over any field that is a splitting field of its minimal polynomial. A number system is constructed which is isomorphic to the factor ring \(\mathbb{C} [\lambda]/ \langle\psi \rangle\) for an arbitrary polynomial \(\psi\).
openaire +2 more sources
Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs
MathematicsAn algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, Cl1,2, and Cl0,3 algebras, there are up to four isolated square roots in a case of the ...
Arturas Acus, Adolfas Dargys
doaj +1 more source
Clifford Algebras and Liquid Crystalline Fermions
Physical Review XWe show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can ...
N. Johnson +8 more
doaj +1 more source
MathematicsThe unital associative algebra structure A on Rn allows for defining elementary functions and functions defined by convergent power series. For these, the usual derivative has a simple form even for higher-order derivatives, which allows us to have the A-
Julio Cesar Avila +2 more
doaj +1 more source
Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm's hidden variables. [PDF]
Sci Rep, 2022 Santilli RM, Sobczyk G.
europepmc +1 more source