Analysis on generalized Clifford algebras

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Abstract

In this article, we study the analysis related to generalized Clifford algebras Cn(a), where a is a non-zero vector. If {e1, . . ., en} is an orthonormal basis, the multiplication is defined by relations (Equation presented) for aj = ej · a. The case a = 0 corresponds to the classical Clifford algebra. We define the Dirac operator as usual by D = Σj ejxj and define regular functions as its null solution. We first study the algebraic properties of the algebra. Then we prove the basic formulas for the Dirac operator and study the properties of regular functions.

Original languageEnglish
Pages (from-to)7-22
Number of pages16
JournalVestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Seriya Fiziko-Matematicheskie Nauki
Volume27
Issue number1
DOIs
Publication statusPublished - 2023
Publication typeA1 Journal article-refereed

Keywords

  • Clifford–Kanzaki algebra
  • Dirac operator
  • generalized Clifford algebra
  • regular function

Publication forum classification

  • Publication forum level 0

ASJC Scopus subject areas

  • Analysis
  • Software
  • Modelling and Simulation
  • Mathematical Physics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Applied Mathematics

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