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Using Periodicity Theorems for Computations in Higher Dimensional Clifford Algebras

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Abstract

We present different methods for symbolic computer algebra computations in higher dimensional (≥ 9) Clifford algebras using CLIFFORD and Bigebra packages for Maple®. This is achieved using graded tensor decompositions, periodicity theorems and matrix spinor representations over Clifford numbers. We show how to code the graded algebra isomorphisms and the main involutions, and we provide some benchmarks.

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Authors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, Box 5054, Cookeville, TN, 38505, U.S.A

    Rafał Abłamowicz

  2. The University of Birmingham, School of Computer Science Edgbaston-Birmingham, B15 2TT, Birmingham, England

    Bertfried Fauser

Authors
  1. Rafał Abłamowicz
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  2. Bertfried Fauser
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Correspondence to Rafał Abłamowicz.

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Abłamowicz, R., Fauser, B. Using Periodicity Theorems for Computations in Higher Dimensional Clifford Algebras. Adv. Appl. Clifford Algebras 24, 569–587 (2014). https://doi.org/10.1007/s00006-014-0440-x

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  • DOI: https://doi.org/10.1007/s00006-014-0440-x

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