Related papers: Infinity-Inner-Products on A-Infinity-Algebras

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A-infinity algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the…

Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke products of type $G$ and of finite type $G$, respectively. Let $E$ and $E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the complex…

We compute the Hochschild Cohomology of a finite-dimensional preprojective algebra of generalized Dynkin type Ln over a field of characteristic different from 2 . In particular, we describe the ring structure of the Hochschild Cohomology…

The product systems over left cancellative small categories are introduced and studied in this paper. We also introduce the notion of compactly aligned product systems over finite aligned left cancellative small categories and its Nica…

The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…

A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…

We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations.…

In \cite{SSZ}, the authors proved that an Artin algebra $A$ with infinite global dimension has an indecomposable module with infinite projective and infinite injective dimension, giving a new characterisation of algebras with finite global…

The derived bracket of a Maurer-Cartan element in a differential graded Lie algebra (DGLA) is well-known to define a differential graded Leibniz algebra. It is also well-known that a Lie infinity morphism between DGLAs maps a Maurer-Cartan…

In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a…

We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums…

We show that the tensor product of two cyclic $A_\infty$-algebras is, in general, not a cyclic $A_\infty$-algebra, but an $A_\infty$-algebra with homotopy inner product. More precisely, we construct an explicit combinatorial diagonal on the…

In this paper, we compute the product structure of the Hochschild cohomology of preprojective algebras of quivers of type D and E over a field of characteristic zero.

We describe semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Consider an associative algebra $A$ and two its subalgebras $B$ and $N$ such that $A=B\otimes N$ as a vector space. We prove that the…

Let $A$ and $B$ be two algebraic quantum groups (i.e. multiplier Hopf algebras with integrals). Assume that $B$ is a right $A$-module algebra and that $A$ is a left $B$-comodule coalgebra. If the action and coaction are matched, it is…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

We study the twisted cohomology groups of $A_\infty$-algebras defined by twisting elements and their behavior under morphisms and homotopies using the bar construction. We define higher Massey products on the cohomology groups of general…

First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew braces, heaps, trusses). Then we analyse the concept of…

Given a two-sided noetherian ring $A$ with a dualizing complex, we show that the big finitistic dimension of $A$ is finite if and only if every bounded below Gorenstein-projective-acyclic cochain complex of Gorenstein-projective $A$-modules…