On the Tits-Kantor-Koecher construction of unital Jordan bimodules

In this paper we explore relationship between representations of a Jordan algebra $\text{J}$ and the Lie algebra $\text{g}$ obtained from $\text{J}$ by the Tits-Kantor-Koecher construction. More precisely, we construct two adjoint functors $Lie:\text{JJ}\to \text{ggm}$ and $Jor:\text{ggm}\to \text{JJ}$, where $\text{JJ}$ is the category of unital $\text{J}$-bimodules and $\text{ggm}$ is the category of $\text{g}$-modules admitting a short grading. Using these functors we classify $\text{J}$ such that its semisimple part is of Clifford type and the category $\text{JJ}$ is tame.