Graded simple Jordan superalgebras of growth one (Q2709433)

Let \(J=\sum_{i\in \mathbb Z}J_i\) be an infinite-dimensional \(\mathbb Z\)-graded simple Jordan superalgebra with a unit element over an algebraically closed field of characteristic zero. It is assumed that \(\dim J_i\), \(i\in \mathbb Z,\) are uniformly bounded. Then \(J\) is one of the following superalgebras:NEWLINENEWLINENEWLINE-- a loop superalgebra of a finite-dimensional simple \(\mathbb Z/n\mathbb Z\)-graded Jordan superalgebra; NEWLINENEWLINENEWLINE-- a Jordan superalgebra of a nondegenerate supersymmetric form in a \(\mathbb Z\)-graded vector space; NEWLINENEWLINENEWLINE-- a Kantor double of an associative commutative superalgebra with a Jordan bracket; NEWLINENEWLINENEWLINE-- a Jordan superalgebra of Cartan type; NEWLINENEWLINENEWLINE-- two exceptional Jordan superalgebras whose Tits-Kantor-Koecher constructions are isomorphic to the exceptional superalgebra \(CK(6)\) of Neveu-Schwarz and Ramond types.NEWLINENEWLINENEWLINEThis result confirms the conjecture of Kac -- van de Leur on a classification of \(\mathbb Z\)-graded simple Lie superalgebras \(L=\sum_{i\in \mathbb Z}L_i\) containing a Virasoro algebra in the even part such that the dimensions of the homogeneous components \(\dim L_i\) are uniformly bounded.