Related papers: A note on Gorenstein spaces

The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory that algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes…

The object of this paper is to show that non-homotopy finite Poincar\'e duality spaces are plentiful. Let $\pi$ be finitely presented group. Assuming that the reduced Grothendieck group $\tilde K_0(\Bbb Z[\pi])$ has a non-trivial…

Artinian quotients R of the local ring Q = k[[x,y,z]] are classified by multiplicative structures on A = Tor_Q^*(R,k); in particular, R is Gorenstein if and only if A is a Poincare duality algebra while R is Golod if and only if all…

This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively…

In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…

We define a new ${\mathbb Z}_2$-graded quantum (2+1)-space and show that the extended ${\mathbb Z}_2$-graded algebra of polynomials on this ${\mathbb Z}_2$-graded quantum space, denoted by ${\cal F}({\mathbb C}_q^{2\vert1})$, is a ${\mathbb…

Let $W$ be a $G$-graded algebra over a field of characteristic zero, where $G$ is a finite group. We develope a theory of generalized $G$-graded polynomial identities satisfied by any finite-dimensional $W$-algebra $A$, by mean of the…

Any $\mathbb{N}$-graded commutative Gorenstein ring $R$ of Krull dimension one with $R_0$ a field admits a standard silting object $V$ in the stable category $\underline{\mathrm{CM}}_0^{\mathbb{Z}}R$, and the object $V$ is tilting if and…

We study the finite generation of homotopy groups of closed manifolds and finite CW-complexes by relating it to the cohomology of their fundamental groups. Our main theorems are as follows: when $X$ is a finite CW-complex of dimension $n$…

In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the $\mathbb{Q}$-vector space $\mathcal{E}xt_{C^{\ast}(X;\mathbb{Q})}(\mathbb{Q},C^{\ast}(X;\mathbb{Q}))$ with a…

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and…

We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…

Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak…

Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and…

Let $A$ be a $Z$-graded associative algebra and let $\rho$ be an irreducible $N$-graded representation of $A$ on $W$ with finite-dimensional homogeneous subspaces. Then it is proved that $\rho(\tilde{A})=gl_{J}(W)$, where $\tilde{A}$ is the…

A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…

We show that if $T$ is any of four semigroups of two elements that are not groups, there exists a finite dimensional associative $T$-graded algebra over a field of characteristic $0$ such that the codimensions of its graded polynomial…

We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem between homology and cohomology that preserves this structure.…

A class of Z_2-graded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated. They have the form g = g_0 + g_1, with g_0 = so(V) + W_0 and g_1 = W_1,…

We provide spectral Lie algebras with enveloping algebras over the operad of little $G$-framed $n$-dimensional disks for any choice of dimension $n$ and structure group $G$, and we describe these objects in two complementary ways. The first…