scholarly journals On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Dmitry Shirokov
Keyword(s):  
Clifford Algebras ◽  
Inner Automorphisms

scholarly journals ON CLIFFORD SUBALGEBRAS, SPACETIME SPLITTINGS AND APPLICATIONS

2006 ◽  
Vol 03 (07) ◽  
pp. 1359-1380 ◽  
Author(s):  
R. DA ROCHA ◽  
J. VAZ
Keyword(s):  
Angular Momentum ◽  
Clifford Algebras ◽  
Operator Splitting ◽  
Differential Forms ◽  
Lie Derivative ◽  
Dirac Spinor ◽  
Direct Sum ◽  
Time Component ◽  
Orthogonal Components ◽  
Inner Automorphisms

ℤ2-gradings of Clifford algebras are reviewed and we shall be concerned with an α-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced α-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Isomorphisms of graded skew Clifford algebras

2020 ◽  
Vol 13 (5) ◽  
pp. 871-878
Author(s):  
Richard G. Chandler ◽  
Nicholas Engel
Keyword(s):  
Clifford Algebras

On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Carlos Daniel Tamayo-Castro ◽  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes
Keyword(s):  
Clifford Algebras ◽  
Monogenic Functions ◽  
Riemann Problems ◽  
Lower Dimensional

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

The classical problem of the charge and pole motion. A satisfactory formalism by Clifford algebras

1989 ◽  
Vol 220 (1-2) ◽  
pp. 195-199 ◽  
Author(s):  
W.A. Rodrigues ◽  
E. Recami ◽  
A. Maia ◽  
M.A.F. Rosa
Keyword(s):  
Clifford Algebras ◽  
Classical Problem ◽  
Pole Motion

A Note on Generalized Clifford Algebras and Representations

1989 ◽  
Vol 17 (1) ◽  
pp. 93-102 ◽  
Author(s):  
S. Caenepeel ◽  
F. Van Oystaeyen
Keyword(s):  
Clifford Algebras

scholarly journals REPRESENTATIONS OF ALTERNATIVE CLIFFORD ALGEBRAS OF QUADRATIC FORMS

2014 ◽  
Vol 57 (3) ◽  
pp. 579-590 ◽  
Author(s):  
STACY MARIE MUSGRAVE
Keyword(s):  
Quadratic Form ◽  
Clifford Algebra ◽  
Algebraic Structure ◽  
Quadratic Forms ◽  
Clifford Algebras ◽  
Future Research ◽  
Octonion Algebras

AbstractThis work defines a new algebraic structure, to be called an alternative Clifford algebra associated to a given quadratic form. I explored its representations, particularly concentrating on connections to the well-understood octonion algebras. I finished by suggesting directions for future research.

Metric and Involution Scores of Clifford Algebras

2016 ◽  
Vol 26 (4) ◽  
pp. 1331-1340 ◽  
Author(s):  
Greg Trayling
Keyword(s):  
Clifford Algebras
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