Related papers: Foundations of algebraic surgery

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…

This is an expository article about operads in homotopy theory written as a chapter for an upcoming book. It concentrates on what the author views as the basic topics in the homotopy theory of operadic algebras: the definition of operads,…

The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…

We classify the primitive ideals of generalized down-up algebras

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

This paper presents a preliminary version of the deformation theory of expressions of elements of algebras. The notion of *-functions is given. Several important problems appear in simplified forms, and these give an intuitive bird's-eye of…

Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…

The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.

This is a cornucopia of types of algebras with some of their properties from the operadic point of view.

This paper introduces a notion of fundamental group appropriate for laminations.

The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.

We obtain a complete classification of minimal simple unitary $W$-algebras.

This short note contains elementary evaluations of some Euler sums.

It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

We introduce the concept of protometric and present some properties of protometrics.

This paper investigates the normal bases of algebras with low growth.

We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.