Structure theorem for Jordan algebra bundles

Abstract

Purpose – The aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles. Design/methodology/approach – Using the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles. Findings – Findings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles. Originality/value – To the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.

Keywords

• Jordan algebra bundle
• Lie algebra bundle
• Vector bundle