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Landsberg, J.M. and Manivel, L. (2004) Representation Theory and Projective Geometry. In: Popov, V.L., Ed., Algebraic Transformation Groups and Algebraic Varieties, Springer, Berlin, 71-122.
https://doi.org/10.1007/978-3-662-05652-3_6

has been cited by the following article:

• TITLE: Dirac and Maxwell Systems in Split Octonions

  AUTHORS: Merab Gogberashvili, Alexandre Gurchumelia

  KEYWORDS: Split Octonions, Triality, SO(4, 4), Dirac and Maxwell Equations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.7, July 26, 2023

  ABSTRACT: The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4 + 4)-space. Split octonionic representation of SO(4, 4) and Spin(4, 4) groups and the trilinear invariant form are explicitly written and compared with Clifford algebraic matrix representation. It is noted that the complete algebra of split octonionic basis units can be recovered from the Moufang and Malcev relations for the three vector-like elements. Lagrangians on split octonionic fields that generalize Dirac and Maxwell systems are constructed using group invariant forms. It is shown that corresponding equations are related to split octonionic analyticity conditions.