相关论文: Algebraic functions and closed braids

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006) and follows its referencing guidelines.

Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371…

Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal,…

This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the…

We show that the principal results of the article "The metric dimension of graph with pendant edges" [Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 139--145] do not hold. In this paper we correct the results…

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…

See math-ph/0205036 for an expanded version.

Correction to The Annals of Statistics (1989) 17 1749--1766 [URL: http://links.jstor.org/sici?sici=0090-5364%28198912%2917%3A4%3C1749%3AEPEFSP%3E 2.0.CO%3B2-9]

This is a paper in Analytic Topology.

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…

An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.

Double pants decompositions were introduced in our paper "Double pants decompositions of 2-surfaces" (Mosc. Math. J. 11 (2011), no. 2, 231-258, arXiv:1005.0073), together with a flip-twist groupoid acting on these decompositions. It was…

This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…

We give a proof of the Radford's Biproduct Theorem in S. Montgomery's book [Hopf Algebras and Their Actions on Rings, CBMS 82, AMS,1993.] by using Majid's braided diagrams method and Yu.Bespalov and V. Lyubashenko's "t-angles.sty" package.

In this note presentations are given for the nilHecke algebras implicit in the work of Bressler and Evens on Schubert calculus for generalized cohomology theories. Such algebras do not usually satisfy the braid relation. Here the…

This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…

We correct a mistake in the construction of push-outs along free morphisms of algebras over a nonsymmetric operad in arXiv:1101.1634 [math.AT], and we fix the affected results in arXiv:1101.1634 [math.AT] and arXiv:1304.6641 [math.AT].

A complete classification of two-dimensional algebras over algebraically closed fields is provided

We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present certain corollaries of this result.

This work is a continuation of what was done in a previous paper and strongly connected to the recent work of U. Abel and I. Rasa [arXiv:1707.00127]