Minimal superalgebras generating minimal supervarieties (Q1706096)

In characteristic zero the generators of the minimal supervarieties of finite basic rank belong to the class of \textit{minimal superalgebras} introduced in [\textit{A. Giambruno} and \textit{M. Zaicev}, Trans. Am. Math. Soc. 355, No. 12, 5091--5117 (2003; Zbl 1031.16015)]. The authors give a complete list of minimal supervarieties generated by minimal superalgebras whose maximal semisimple homogeneous subalgebra is the sum of three graded simple algebras. As a consequence, they give a negative answer to the question of whether any minimal superalgebra generates a minimal supervariety.