Abstract
Giambruno and Zaicev stated that, over a field of characteristic zero, T-ideals of minimal varieties of a fixed exponent have the factoring property. In the present article, we describe necessary and sufficient conditions for the factorability of T2-ideals of minimal supervarieties of a fixed superexponent. In light of the characterization of minimal supervarieties of a fixed superexponent given by Di Vincenzo, da Silva, and Spinelli, the crucial point is the study of the factorability of T2-ideals of the upper-block triangular matrix algebras equipped with an elementary
-grading, where
are simple superalgebras. We obtain necessary and sufficient conditions for the isomorphism between two superalgebras
. We also show that the concept of
-regularity establishes a nice connection between the factorability of the T2-ideal of
and the number of isomorphism classes of
.
Acknowledgements
We would like to express our gratitude to Professor Antonio Giambruno for proposing us this problem.