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In this paper we calculate the Hochschild cohomology of gentle $A_\infty$-algebras of arc collections on marked surfaces without boundary components. When the underlying arc collection has no loops or two-cycles, we show that the dgla…
We work over an o-minimal expansion of a real closed field. The o-minimal homotopy groups of a definable set are defined naturally using definable continuous maps. We prove that any two semialgebraic maps which are definably homotopic are…
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. A theory of deformations for associative algebras is presented. Closed left ideal generated by…
Hom-bialgebras and Hom-Hopf algebras are generalizations of bialgebra and Hopf algebra structures, where associativity and coassociativity conditions are twisted by a homomorphism. The purpose of this paper is to define a…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
Abstract: We show that boundary string field theory realizes the minimal model of open string field theory. More precisely, we observe that the expansion of the (co)homological vector field, $Q$ of boundary string field theory in the…
We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…
We apply stochastic quantization method to Kostov's matrix-vector models for the second quantization of orientable strings with Chan-Paton like factors, including both open and closed strings. The Fokker-Planck hamiltonian deduces an…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal, Costello, and Hopkins and Lurie, on "open-closed topological conformal field theories". Given a…
We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of \epsilon_1 and \epsilon_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's…
This paper generalizes Huang's cohomology theory of grading-restricted vertex algebras to meromorphic open-string vertex algebras (MOSVAs hereafter), which are noncommutative generalizations of grading-restricted vertex algebras introduced…
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over…
We give a brief summary of algebraic aspects of string theory arising in the noncommutative geometry setting of foliations called string diagrammatics which we introduced jointly with Bob Penner. We furthermore discuss how this gives rise…
To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of…
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
We obtain the spectrum of heterotic strings compactified on orbifolds, focusing on its algebraic structure. Affine Lie algebra provides its current algebra and representations. In particular the twisted spectrum and the Abelian charge are…
In this paper we define a new cohomology theory for a $B$-algebra $A$. We use this cohomology to study deformations of algebras $A[[t]]$, that have a $B$-algebra structure.
The purpose of this paper is to define an $\alpha$-type cohomology, which we call $\alpha$-type Chevalley-Eilenberg cohomology, for Hom-Lie algebras. We relate it to the known Chevalley-Eilenberg cohomology and provide explicit computations…