Central extensions of axial algebras
Ivan Kaygorodov, C\'andido Mart\'in Gonz\'alez, Pilar P\'aez-Guill\'an

TL;DR
This paper extends the method of Skjelbred-Sund to construct and analyze central extensions of axial algebras, proving splitting results for complex simple Jordan cases and classifying low-dimensional examples.
Contribution
It introduces a new adaptation of the Skjelbred-Sund method for axial algebras and provides classification and splitting results for specific cases.
Findings
All axial central extensions of complex simple finite-dimensional Jordan algebras are split.
Non-split axial central extensions of dimension ≤ 4 are Jordan.
A classification of 2-dimensional axial algebras is provided.
Abstract
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 over an algebraically closed field of characteristic not are Jordan. Also, we give a classification of -dimensional axial algebras and describe some important properties of these algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Synthesis and properties of polymers
