Gelfand-Kirillov dimension and local finiteness of Jordan
superpairs covered by grids and their associated Lie superalgebras
In this paper we show that a Lie superalgebra L graded by a
3-graded irreducible root system has Gelfand-Kirillov dimension equal to
the Gelfand-Kirillov dimension of its coordinate superalgebra A, and
that L is locally finite if and only A is so. Since these Lie
superalgebras are coverings of Tits-Kantor-Koecher superalgebras of
Jordan superpairs covered by a connected grid, we obtain our theorem by
combining two other results. Firstly, we study the transfer of the
Gelfand-Kirillov dimension and of local finiteness between these Lie
superalgebras and their associated Jordan superpairs, and secondly, we
prove the analogous result for Jordan superpairs: the Gelfand-Kirillov
dimension of a Jordan superpair V covered by a connected grid coincides
with the Gelfand-Kirillov dimension of its coordinate superalgebra A,
and V is locally finite if and only if A is so.
E. Garcia < egarciag@mat.ucm.es >
E. Neher < neher@uottawa.ca >