Free Jordan Algebras and Representations of ${\widehat{\mathfrak{sl}}}_2(J)$

Michael Lau, Olivier Mathieu

Let $J$ be a unital Jordan algebra, and let ${\widehat{\mathfrak{sl}}}_2(J)$ be the universal central extension of its Tits-Kantor-Koecher Lie algebra. In Part A, we study the catego…