2022/11/01 by Ivan Kaygorodov, Kaygorodov, Ivan, Cándido Martı́n González +3
Mathematics · Materials Science · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Synthesis and properties of polymers
paper · pdf · doi:10.48550/arxiv.2211.00334
In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split and that all non-split axial central extensions of dimension n≤ 4 over an algebraically closed field of characteristic not 2 are Jordan. Also, we give a classification of 2-dimensional axial algebras and describe some important properties of these algebras.