Related papers: Associahedra, cellular W-construction and products…

Let C_*(K) denote the cellular chains on the Stasheff associahedra. We construct an explicit combinatorial diagonal \Delta : C_*(K) --> C_*(K) \otimes C_*(K); consequently, we obtain an explicit diagonal on the A_\infty-operad. We apply the…

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 construct a cellular complex which is an infinite analogue to Stasheff's associahedra. We prove that it is contractible and state that its (combinatorial) automorphism group is isomorphic to a semi-direct product of R.J.…

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 define a cellular approximation for the diagonal of the Forcey--Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra.…

We give a topological solution to the $\Ainf$ Deligne conjecture using associahedra and cyclohedra. For this we construct three CW complexes whose cells are indexed by products of polytopes. Giving new explicit realizations of the polytopes…

We give a new, construction-free proof of the associativity of tensor product for modules for rational vertex operator algebras under certain convergence conditions.

This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of $P(z)$-tensor products for nonzero complex numbers $z$ constructed…

The paper is devoted to explaining the operadic meaning of freehedra, a family of polytopes originally defined to study free loop spaces. We introduce the notion of operadic pairs and algebras over them. Cellular chains on Stasheff…

We define a collection of tensor product norms for C*-algebras and show that a symmetric tensor product functor on the category of separable C*-algebras need not be associative.

Let $\otimes$ be the map which classifies the tensor product of two line bundles, an extension of this map to the space of all codimension 1 algebraic cycles is constructed. It is proved that this extension cannot exist in codimension…

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A-infinity algebras of Fukaya-Oh-Ohta-Ono.

Extending work of Saneblidze-Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of A-infinity algebras, modules, algebra homomorphisms, and module morphisms, as well as to define a bimodule…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We show that for $q\not=-1$ the q-graded tensor product fails to preserve the q-differential structure of the product algebra and therefore there is no natural tensor product construction for q-differential algebras.

Given two cyclic A$_\infty$-algebras $A$ and $B$, we prove that there exists a cyclic A$_\infty$-algebra structure on their tensor product $A\otimes B$ which is unique up to a cyclic A$_\infty$-quasi-isomorphism. Furthermore, the Kontsevich…

We construct an A-infinity structure on the tensor product of two A-infinity algebras by using the simplicial decomposition of the Stasheff polytope. The key point is the construction of an operad AA-infinity based on the simplicial…

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the…

We construct an explicit diagonal \Delta_P on the permutahedra P. Related diagonals on the multiplihedra J and the associahedra K are induced by Tonks' projection P --> K and its factorization through J. We introduce the notion of a…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…