ﻻ يوجد ملخص باللغة العربية
This paper is based on the authors paper Koszul duality in deformation quantization, I, with some improvements. In particular, an Introduction is added, and the convergence of the spectral sequence in Lemma 2.1 is rigorously proven. Some informal discussion in Section 1.5 is added.
We develop an elementary method for proving the PBW theorem for associative algebras with an ascending filtration. The idea is roughly the following. At first, we deduce a proof of the PBW property for the {it ascending} filtration (with the filtered
Let $n geq 2$ be an integer. An emph{$n$-potent} is an element $e$ of a ring $R$ such that $e^n = e$. In this paper, we study $n$-potents in matrices over $R$ and use them to construct an abelian group $K_0^n(R)$. If $A$ is a complex algebra, there i
We discuss a version of the Chevalley--Eilenberg cohomology in characteristic $2$, where the alternating cochains are replaced by symmetric ones.
We consider a class of extensions of both abstract and pseudocompact algebras, which we refer to as strongly proj-bounded extensions. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by
Using combinatorics of chains going back to works of Anick, Green, Happel and Zacharia, we give, for any monomial algebra $A$, an explicit description of its minimal model. This also provides us with formulas for a canonical $A_infty$-structure on th