Results 1 
2 of
2
AInfinity Algebras in Representation Theory
, 2001
"... We give a brief introduction to A1algebras and show three contexts in which they appear in representation theory: the study of Yoneda algebras and Koszulity, the description of categories of ltered modules and the description of triangulated categories. Contents 1. Denitions, the bar construction, ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We give a brief introduction to A1algebras and show three contexts in which they appear in representation theory: the study of Yoneda algebras and Koszulity, the description of categories of ltered modules and the description of triangulated categories. Contents 1. Denitions, the bar construction, the minimality theorem 1 2. Yoneda algebras, Koszulity and ltered modules 5 3. Description of triangulated categories 8 References 10 1. Definitions, the bar construction, the minimality theorem 1.1. Ainnity algebras and morphisms. We refer to [11] for a list of references and a topological motivation for the following denition: Let k be a eld. An A1  algebra over k is a Zgraded vector space A = M p2Z A p endowed with graded maps (=homogeneous klinear maps) mn : A
"Coalgebra" Structures on 1Homological Models for Commutative Differential Graded Algebras
"... In [3] "mall" 1homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [79] provides an explicit description of an A1coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map ..."
Abstract
 Add to MetaCart
In [3] "mall" 1homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [79] provides an explicit description of an A1coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map 2 : H ! H H as a first step in the study of this structure. Developing the techniques given in [20] (inversion theory), we get an important improvement in the computation of 2 with regard to the first formula given by HPT. In the case of purely quadratic algebras, we sketch a procedure for giving the complete Hopf algebra structure of its 1homology.