Related papers: The pong algebra
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial classification of Hom-algebras over a PROP…
We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.
In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are…
A major challenge in the study of the structure of the three-dimensional homology cobordism group is to understand the interaction between hyperbolic geometry and homology cobordism. In this paper, for a hyperbolic homology sphere $Y$ we…
Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…
This paper is a short introduction to the combinatorial version of tangle Floer homology defined in "Combinatorial tangle Floer homology". There are two equivalent definitions---one in terms of strand diagrams, and one in terms of bordered…
This text gives a construction of a differential graded Lie algebra in Nori's category of effective homological motives. In fact the construction works in more a general setting than that of an Abelian category. This allows us to give the…
An A-infinity bialgebra of type (m,n) is a Hopf algebra H equipped with a "compatible" operation \omega : H^{\otimes m} \to H^{\otimes n} of positive degree. We determine the structure relations for A-infinity bialgebras of type (m,n) and…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decomposition to renormalize multiple polylogarithms at…
The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted by homomorphisms. We discuss…
We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…
We define a higher analogue of Dirac structures on a manifold M. Under a regularity assumption, higher Dirac structures can be described by a foliation and a (not necessarily closed, non-unique) differential form on M, and are equivalent to…
We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by…
Given a commutative algebra $A$ and a quotient $A$-algebra $A/I$, we construct a resolution of $A/I$ as an $A$-module such that it is also a differential graded (dg) algebra with divided powers (PD). This construction makes use of symmetric…
We propose the notion of semi-infinite homology for algebras over operads using the relative homology theory for operadic algebras.
We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with the number of nodes. Furthermore, we show that when the…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
Building on Kadeishvili's original theorem inducing $A_\infty$-algebra structures on the homology of dg-algebras, several directions of algorithmic research in $A_\infty$-algebras have been pursued. In this paper we will survey work done on…