Related papers: A Hilton-Milner theorem for exterior algebras

In this short note we show that both generalizations of celebrated Erd\H{o}s--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from the folklore puzzle about…

The Erd\H{o}s--Ko--Rado theorem is extended to designs in semilattices with certain conditions. As an application, we show the intersection theorems for the Hamming schemes, the Johnson schemes, bilinear forms schemes, Grassmann schemes,…

We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topology, and the study of…

Using algebraic cycles as a medium, we prove that the groups of the big (Hesselholt-Madsen) de Rham-Witt forms over arbitrary fields are isomorphic to the relative improved (Gabber-Kerz) Milnor $K$-groups of Artin local algebras of…

For an arbitrary field $k$, and an arbitrary regular henselian local $k$-scheme $X$ of dimension $1$ with the residue field $k$, we introduce two subcomplexes of the higher Chow complexes of $X$ using certain extended face intersection…

We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. Using initial monomials, projections of the…

The purpose of this short note is to consider multi-variate Hasse-Schmidt derivations on exterior algebras and to show how they easily provide remarkable identities, holding in the algebra of square matrices, which generalise the classical…

The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two versions of the Cartan-K\"ahler theorem in the case where the…

Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em each endomorphism…

Our results are of three types. First we describe a general procedure of adjoining polynomial variables to $A_\infty$-ring spectra whose coefficient rings satisfy certain restrictions.A host of examples of such spectra is provided by…

Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants.…

We give a lower bound on the Hilbert series of the exterior algebra modulo a principal ideal generated by a generic form of odd degree and disprove a conjecture by Moreno-Soc\'ias and Snellman. We also show that the lower bound is equal to…

We recall some basic computations in the Milnor-Witt K-theory of a field, following Morel. We then focus on the Witt K-theory of a field of characteristic two and give an elementary proof of the fact that it is isomorphic as a graded ring…

Green's general hyperplane restriction theorem gives a sharp upper bound for the Hilbert function of a standard graded algebra over and infinite field K modulo a general linear form. We strengthen Green's result by showing that the linear…

We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersection. Thus, near-cones of sufficiently high depth satisfy…

We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$

We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be…

We advance the understanding of K-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K-groups and Witt-groups. By an explicit computation of the slice spectral sequence for higher Witt-theory, we…

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.