Lie triple 2-algebras

Abstract

We invent a new cohomology theory for Lie triple algebras. Using this cohomology, we introduce the notions of 2-term $L_{\infty }$-triple algebras and Lie triple 2-algebras. We prove that the category of 2-term $L_{\infty }$-triple algebras is equivalent to the category of Lie triple 2-algebras. Crossed modules of Lie triple algebras are studied in detail.

28 pages that are done in 2023, arXiv admin note: text overlap with arXiv:1601.01196 by other authors