In this paper, the smallest such integer k is called by the index (of nilpotence) of B such that B = 0. In this paper, we study sign patterns allowing nilpotence of index k and obtain four methods to construct sign patterns allowing nilpotence of index at most k, which generalizes some recent results.

This talk covers most of section 4 in the Mathew-Naumann-Noel paper [MNN15]. We first discuss nilpotence in an arbitrary symmetric monoidal stable ∞-category. We then discuss the historical origins of nilpotence in the stable homotopy category, namely the Ravenel conjectures and the Nilpotence theorem proved by Devinatz-Hopkins-Smith.

We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1,C). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. We study the relationships between these results and the combinatorics of Dyck paths, based upon a remarkable bijection between ad-nilpotent ideals an...

While all of the relations in the Steenrod algebra, A, can be deduced in principle from the Adem relations, in practice, it is extremely difficult to determine whether a given polynomial of elements in A is zero for all but the most elementary cases. In his original paper [Mi] Milnor states “It would be interesting to discover a complete set of relations between the given generators of A”. In p...

In this paper we show that any finite algebra A satisfying a weak left nilpotence condition has the property that all maximal subuniverses are congruence blocks. Conversely, if every subalgebra of A has the property that all maximal subuniverses are congruence blocks, then A satisfies the aforementioned nilpotence condition.

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.

Let G be a finite p-group. We say that G has a Johnson polynomial if there exists a polynomial f(x) ∈ Q[x] and a character χ ∈ Irr(G) so that f(χ) equals the total character for G. In this paper, we show that if G has nilpotence class 2, then G has a Johnson polynomial if and only if Z(G) is cyclic, and we show that if |cd(G)| = 2, then G has a Johnson polynomial if and only if G has nilpotence...