Matches in SemOpenAlex for { <https://semopenalex.org/work/W1566364198> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W1566364198 abstract "Construction of a universal finite-type invariant can be reduced, under suitable assumptions, to the solution of certain equations (the hexagon and pentagon equations) in a particular graded associative algebra of chord diagrams. An explicit, closed-form solution to these equations may, indirectly, give information about various interesting properties of knots, such as which knots are ribbon. However, while closed-form solutions (as opposed to solutions which can only be approximated to successively higher degrees) are needed for this purpose, such solutions have proven elusive, partly as a result of the non-commutative nature of the algebra. To make the problem more tractable, we restrict our attention to solutions of the equations in the subalgebra of horizontal chord diagrams, viewed as a graded unital permutative algebra -- where `permutative' means that u[x,y]=0 whenever u has degree at least 1. We show that this restriction leads in a straightforward and fairly short way to a reduction of the hexagon and pentagon equations to a simpler equation taken over the algebra of power series in two commuting variables. This equation had been found and solved explicitly by Kurlin under a superficially different set of reduction assumptions, which we show here are in fact equivalent to ours. This paper thus provides an alternative (simpler and shorter) derivation of Kurlin's equation." @default.
- W1566364198 created "2016-06-24" @default.
- W1566364198 creator A5022585138 @default.
- W1566364198 date "2013-04-16" @default.
- W1566364198 modified "2023-10-18" @default.
- W1566364198 title "Closed-Form Associators in Permutative Chord Diagrams" @default.
- W1566364198 cites W1980518701 @default.
- W1566364198 cites W2038509897 @default.
- W1566364198 cites W2086114750 @default.
- W1566364198 cites W2158942530 @default.
- W1566364198 cites W2492689206 @default.
- W1566364198 cites W2607743015 @default.
- W1566364198 hasPublicationYear "2013" @default.
- W1566364198 type Work @default.
- W1566364198 sameAs 1566364198 @default.
- W1566364198 citedByCount "0" @default.
- W1566364198 crossrefType "posted-content" @default.
- W1566364198 hasAuthorship W1566364198A5022585138 @default.
- W1566364198 hasConcept C136119220 @default.
- W1566364198 hasConcept C159423971 @default.
- W1566364198 hasConcept C183778304 @default.
- W1566364198 hasConcept C190470478 @default.
- W1566364198 hasConcept C202444582 @default.
- W1566364198 hasConcept C2524010 @default.
- W1566364198 hasConcept C2779965921 @default.
- W1566364198 hasConcept C33923547 @default.
- W1566364198 hasConcept C37914503 @default.
- W1566364198 hasConcept C67996461 @default.
- W1566364198 hasConceptScore W1566364198C136119220 @default.
- W1566364198 hasConceptScore W1566364198C159423971 @default.
- W1566364198 hasConceptScore W1566364198C183778304 @default.
- W1566364198 hasConceptScore W1566364198C190470478 @default.
- W1566364198 hasConceptScore W1566364198C202444582 @default.
- W1566364198 hasConceptScore W1566364198C2524010 @default.
- W1566364198 hasConceptScore W1566364198C2779965921 @default.
- W1566364198 hasConceptScore W1566364198C33923547 @default.
- W1566364198 hasConceptScore W1566364198C37914503 @default.
- W1566364198 hasConceptScore W1566364198C67996461 @default.
- W1566364198 hasLocation W15663641981 @default.
- W1566364198 hasOpenAccess W1566364198 @default.
- W1566364198 hasPrimaryLocation W15663641981 @default.
- W1566364198 hasRelatedWork W13448296 @default.
- W1566364198 hasRelatedWork W1518385856 @default.
- W1566364198 hasRelatedWork W1891117966 @default.
- W1566364198 hasRelatedWork W1998030439 @default.
- W1566364198 hasRelatedWork W2007946452 @default.
- W1566364198 hasRelatedWork W2017941472 @default.
- W1566364198 hasRelatedWork W2065369291 @default.
- W1566364198 hasRelatedWork W2115145127 @default.
- W1566364198 hasRelatedWork W2232416236 @default.
- W1566364198 hasRelatedWork W2266634414 @default.
- W1566364198 hasRelatedWork W2299992415 @default.
- W1566364198 hasRelatedWork W2323500172 @default.
- W1566364198 hasRelatedWork W2464411078 @default.
- W1566364198 hasRelatedWork W2493195292 @default.
- W1566364198 hasRelatedWork W2950446711 @default.
- W1566364198 hasRelatedWork W2953069571 @default.
- W1566364198 hasRelatedWork W3108660119 @default.
- W1566364198 hasRelatedWork W3207830705 @default.
- W1566364198 hasRelatedWork W70775824 @default.
- W1566364198 hasRelatedWork W3126838002 @default.
- W1566364198 isParatext "false" @default.
- W1566364198 isRetracted "false" @default.
- W1566364198 magId "1566364198" @default.
- W1566364198 workType "article" @default.