Related papers: Chain homogeneous Souslin algebras

We introduce the concept of an infinite cochain sequence and initiate a theory of homological algebra for them. We show how these sequences simplify and improve the construction of infinite coclass families (as introduced by Eick and…

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…

We show that finite-dimensional order unit spaces equipped with a continuous sequential product as defined by Gudder and Greechie are homogeneous and self-dual. As a consequence of the Koecher-Vinberg theorem these spaces therefore…

Recently, Peeva and the second author constructed irreducible projective varieties with regularity much larger than their degree, yielding counterexamples to the Eisenbud-Goto Conjecture. Their construction involved two new ideas: Rees-like…

We prove that the category of dg-coalgebras is symmetric monoidal closed and that the category of dg-algebras is enriched, tensored, cotensored and strongly monoidal over that of coalgebras. We apply this formalism to reconstruct several…

Anick proved that every q-mild Hopf algebra up to homotopy is isomorphic to a primitively-generated chain Hopf algebra. We provide a new proof, that involves extensive use of the Bockstein spectral sequence.

Answering a question of H. Petersson, we provide a class of examples of pair of octonion algebras over a ring having isometric norms.

A homogeneous symmetric structure on an associative superalgebra A is a non-degenerate, supersymmetric, homogeneous (i.e. even or odd) and associative bilinear form on A. In this paper, we show that any associative superalgebra with non…

The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order,…

We obtain sufficient criteria for simplicity of systems, that is, rings $R$ that are equipped with a family of additive subgroups $R_s$, for $s \in S$, where $S$ is a semigroup, satisfying $R = \sum_{s \in S} R_s$ and $R_s R_t \subseteq…

In this paper, we prove that the product of a paired calibrated set and a set of codimension 1 calibrated by a coflat calibration with small singularity set is Almgren minimal. This is motivated by the attempt to classify all possible…

Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are…

We show that the basic categorical concept of an S-algebra as derived from the theory of Segal's Gamma-sets provides a unifying description of several constructions attempting to model an algebraic geometry over the absolute point. It…

We consider Arveson's problem on the maximality of subdiagonal algebras. We prove that a subdiagonal algebra is maximal if it is invariant under the modular group of a faithful normal state which is preserved by the conditional expectation…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

Let $A$ be an Artinian Gorenstein algebra over an infinite field $k$ with either $\hbox{char}(k)=0$ or $\hbox{char}(k)>\nu$, where $\nu$ is the socle degree of $A$. To every such algebra and a linear projection $\pi$ on its maximal ideal…

In this article we classify all infinitesimal Hecke algebras of so_N. We establish isomorphism of their universal versions and the W-algebras of so_{N+2m+1} with a 1-block nilpotent element of the Jordan type (1,...,1,2m+1). This should be…

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible…