In the present paper it is proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed $ast$-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary $Z_2$-grading and graded involution.
Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B G be a Borel
subgroup. Then B acts with finitely many orbits on the variety N2 of the nilpotent elements whose height is at most 2. We provide a parametrization of the B-orbits in N2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.
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