Rotations in the Space of Split Octonions. (16th June 2009)

• Record Type: Journal Article
• Authors: Gogberashvili, Merab
• Other Names: Lizzi Fedele Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2009(2009)
• Publication Date: 2009-06-16
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2009/483079
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic "eight-space" are not equivalent. The group of passive transformations that leave invariant the pseudonorm of split octonions isS O ( 4, 4 ), while active rotations are done by the direct product ofO ( 3, 4 ) -boosts and real noncompact form of the exceptional groupG 2 . In classical limit, these transformations reduce to the standard Lorentz group.