Ternary Clifford Algebras

Abstract

Ternary Clifford algebras are an essential ingredient in a cubic factorization of the Laplacian and using a ternary Clifford analysis build on such spaces one obtains a Dirac-type operator D such that \(D^3=\Delta \). This paper is a continuation of the work of the authors in describing properties of generalized ternary Clifford algebras. Here we explore a blade decomposition and symmetries of these algebras.

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Acknowledgements

The work of P. Cerejeiras was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project references UIDB/04106/2020 and UIDP/04106/2020 as well as under the FCT Sabbatical grant ref. SFRH/BSAB/143104/2018. The authors would also like to thank the anonymous referees for their input. These relevant discussions contributed greatly towards the improvement of this manuscript.

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This article is part of the Topical Collection on ISAAC 12 at Aveiro, July 29-August 2, 2019, edited by Swanhild Bernstein, Uwe Kaehler, Irene Sabadini, and Franciscus Sommen.

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Cerejeiras, P., Vajiac, M. Ternary Clifford Algebras. Adv. Appl. Clifford Algebras 31, 13 (2021). https://doi.org/10.1007/s00006-020-01114-3

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Mathematics Subject Classification

  • Primary 30G35
  • Secondary 26A33
  • 30A05
  • 31B05