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

In this paper we explore relationship between representations of a Jordan algebra J and the Lie algebra g obtained from J by the Tits-Kantor-Koecher construction. More precisely, we construct two adjoint functors Lie:J-mod1→g-mod1 and Jor:g-mod1→J-mod1, where J-mod1 is the category of unital J-bimodules and g-mod1 is the category of g-modules admitting a short grading. Using these functors we classify J such that the semisimple part is of Clifford type and the category J-mod1 is tame.