Related papers: On the construction of A-infinity structures
We discuss that there exist at least two different choices in the signs of the induced A-infinity structures in shifting the degree of objects in an A-infinity category. We show that both of these choices are naturalin the sense that they…
An associative algebra is nothing but an odd quadratic codifferential on the tensor coalgebra of a vector space, and an A-infinity algebra is simply an arbitrary odd codifferential. Hochschild cohomology classifies the deformations of an…
An A-infinity algebra is a generalization of a associative algebra, and an L-infinity algebra is a generalization of a Lie algebra. In this paper, we show that an L-infinity algebra with an invariant inner product determines a cycle in the…
This is an expanded comment on Barannikov's paper math.AG/0006193. A symplectic version of his construction is discussed. It is shown that the duality transformation for mirror torus fibrations over the same Monge-Ampere manifold exchanges…
In this paper the Hochschild-cochain-complex of an A-infinity-algebra A with values in an A-infinity-bimodule M over A and maps between them is defined. Then, an infinity-inner-product on A is defined to be an A-infinity-bimodule-map…
This is the author's diploma thesis. In the first part of the thesis the algebra structure on the Ext-spaces Ext^k(M(x), M(y)) of Verma modules M(x) and M(y) in the parabolic category O for the case of the parabolic subalgebras gl(n) x…
The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of…
Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras…
A general construction of integrable hierarchies based on affine Lie algebras is presented. The models are specified according to some algebraic data and their time evolution is obtained from solutions of the zero curvature condition. Such…
We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
We study higher depth algebras. We introduce several examples of such structures starting from the notion of $N$-differential graded algebras and build up to the concept of $A_{\infty}^N$-algebras.
We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its…
Let M be a graded Lie algebra, together with graded Lie subalgebras L and A such that as a graded space M is the direct sum of L and A, and A is abelian. Let D be a degree one derivation of M squaring to zero and sending L into itself, then…
In this paper we will study deformations of A-infinity algebras. We will also answer questions relating to Moore algebras which are one of the simplest nontrivial examples of an A-infinity algebra. We will compute the Hochschild cohomology…
The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set…
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
Introducing Nijenhuis forms on Lie-infinity algebras gives a general frame to understand deformations of the latter. We give here a Nijenhuis interpretation of a deformation of an arbitrary Lie algebroid into a Lie-infinity algebra. Then we…
We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…