We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré du-ality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.

We present a nontrivial extension to Bose's method for the construction of Steiner triple systems, generalizing the traditional use of commutative and idempotent quasi-groups to employ a new algebraic structure called a 3-triangulation. Links between Steiner triple systems and 2-(v,3,3) designs via 3-triangulations are also explored.

In this paper we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by Crawley-Boevey and Shaw carry a natural Poisson structure. This follows the fact that appropriately localized path algebras of double quivers carry a certain kind of non-commutative quasi-Hamiltonian structure.

We derive explicit expressions for the generating series of the fundamental solutions of the Ar quantum Q-system of Di Francesco and Kedem [Non-commutative integrability, paths and quasi-determinants, Adv. in Math. 228(1) (2011) 97–152], expressed in terms of any admissible initial data. These involve products of quantum multinomial coefficients, coded by the initial data structure.

This paper describes a simple candidate one-way hash function which satisfies a quasi-commutative property that allows it to be used aa an accumulator. This property allows protocols to be developed in which the need for a trusted central authority can be eliminated. Spaceefficient distributed protocols are given for document time stamping and for membership testing, and many other applications...

Let R be a commutative ring, (f) an ideal of R, and E = K(f ;R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T , the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

The aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎It is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

Quasi-hereditary algebras can be viewed as a Lie theory approach to the theory of finite dimensional algebras. Motivated by the existence of certain nice bases for representations of semisimple Lie algebras and algebraic groups, we will construct in this paper nice bases for (split) quasi-hereditary algebras and characterize them using these bases. We first introduce the notion of a standardly ...

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is de ned by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical su ciency ...