Related papers: Blackbox computation of $A_\infty$-algebras
One of the main tools to classify \cst-algebras is the study of its projections and its unitaries. It was proved by Cuntz in \cite{Cu81} that if $A$ is a \textit{purely infinite} simple \cst-algebra, then the kernel of the natural map for…
An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {\omega^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,\omega^{1,i}) is an A_\infty-algebra and (H,\omega^{j,1}) is an A_\infty-coalgebra. Structural…
Given a simple vertex algebra A and a reductive group G of automorphisms of A, the invariant subalgebra A^G is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally not true…
This paper investigates if a differential graded algebra can have more than one $A_\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\infty$-structure up…
We prove explit formulas for the decomposition of a differential graded Lie algebra into a minimal and a linear $L_\infty$-algebra. We define a category of metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the…
We study certain modules over the algebra of a Cartier divisor on a scheme. Using these modules, we present an inductive method for studying finite generation properties of algebras and modules. In the context of the minimal model program,…
Kadeishvili's minimal model theorem establishes the existence of an $A_\infty$-structure, unique up to isomorphism, on the cohomology of a dg associative algebra, which captures its homotopy type. In this note we prove the existence of…
In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
We describe cohomological conditions that are necessary and sufficient for the existence of balanced dualizing dg-modules, generalizing a theorem of Van den Bergh for balanced dualizing complexes over graded algebras. As a consequence, we…
The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
Kontsevich and Soibelman has proved a relation between a non-degenerate cyclic homology element of an A-infinity algebra A and its cyclic inner products on the minimal model of A. We find an explicit formula of this correspondence, in terms…
To any periodic module over any algebra, this paper introduces an associated trivial extension DG-algebra T. After first passing to a strictly unital $A_\infty$-minimal model, it then constructs a particular $A_\infty$-algebra N, called the…
Using the classification theorem due to Kac we prove that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by one element.
In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…
We present news proofs of the additivity, resolution and cofinality theorems for the algebraic $K$-theory of exact categories. These proofs are entirely algebraic, based on Grayson's presentation of higher algebraic $K$-groups via binary…
This paper introduces and investigates some properties of algebras constructed from the algebra of polynomials via derivation and integration operators using a process presented by Dzhumadildaev in a previous work. In particular, we…
We present an elementary and self-contained construction of $A_\infty$-algebras, $A_\infty$-bimodules and their Hochschild homology and cohomology groups. In addition, we discuss the cup product in Hochschild cohomology and the spectral…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…