2 The “algebra” K[[x]] ⋊ M of formal power series under multiplication and substitution 3 2.1 Basics on formal power series . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 “Algebra” of formal power series under substitution . . . . . . . . . . . . 4 2.2.1 Right-distributive algebras . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Substitution of formal power series . . . . . . . . . ....

2 The Riordan skew algebra K[[x]] ⋊ M of formal power series under multiplication and substitution 3 2.1 Basics on formal power series . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Skew algebra of formal power series under substitution . . . . . . . . . . 4 2.2.1 Right-distributive algebras . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Substitution of formal power series . . . . ....

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective s...

Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of non local operators that resembles the order-disorder dual algebra of ’t Hooft. These dual operators provide a complete description of the physical phase sp...

We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the original conjecture for topological vertex operator algebras. We illustrate the usefulness of our main tools, operads and “string vertices” by obtaining new results on Vassiliev invariants of knots and double...

In the case of the field C, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the field but this will be too coarse to give a differentiable structure. A celebrated example of how partial algebraic and topological data (G a locally euclidean group) determines a differentiable structure (G is a Lie group) is Hilbert’s 5th p...

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a Pseudo-Anosov mapping class. Our calculations are compatible with all known calculations of...

This paper presents dual B-topologies that are determined by filterbase and some sets in a B-algebra. Also, properties of B-topological space provided. In particular, commutative symmetric topological B-algebras.