Abstract We consider algebraic varieties canonically associated with any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus nilpotent elements (the projectivized parity reversal of) odd part algebra. Most these have appeared various guises previous literature, but we systematically here, from a new perspective: As natural moduli space...

I generalize the standard notion of the composition g ◦ f of correspondences f : X → Y and g : Y → Z to the case that X and Z are arbitrary varieties but Y is smooth and projective. Using this notion, I give a short self-contained proof of Rost’s “nilpotence theorem” and a generalization of one important result used by Rost in his proof of the nilpotence theorem.

It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...

We prove that any rigid additive symmetric monoidal category can be mapped to a abelian in universal way. This yields novel approach Grothendieck's standard conjecture D and Voevodsky's smash nilpotence conjecture.

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated...

In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a algebra over field of zero characteristic satisfies identity some unexpected “universal” identities, in particular, right associator nilpotence, and nilpotence the commutator ideal. This, implies if only it is Lie-solvable. also establish any system identities follows from finitely many them, same holds fo...