. "3"^^ . "1"^^ . "IAA1019203" . . "Homotopy invariant structures in algebra"@en . "Konstrukce rezolventy PROPu pro bialgebry. Formulace obecn\u00E9 teorie vy\u0161\u0161\u00EDch homotopick\u00FDch operac\u00ED. Charakterizace homotopick\u00E9ho typu voln\u00FDch prostor\u016F smy\u010Dek. Explicitn\u00ED formule pro ide\u00E1ln\u00ED perturba\u010Dn\u00ED lemma v kat. siln\u011B homotop. asociativn\u00EDch algeber."@cs . . "Teorie homotopicky invariantn\u00EDch struktur v topologii byla rozvinuta M Boardmanem a R. Vogtem v roce 1973. Prvn\u00ED systematick\u00FD pokus vytvo\u0159it analogickou teorii pro algebraick\u00E9 struktury byl u\u010Din\u011Bn mnohem pozd\u011Bji, v roce 1999 v \u017Eadatelov\u011B \u010Dl\u00E1nku %22Homotopy algebras are homotopy algebras%22. Metody tohoto \u010Dl\u00E1nku byly ji\u017E \u00FAsp\u011B\u0161n\u011B aplikov\u00E1ny nap\u0159. v Kontsevi\u010Dov\u011B d\u016Fkazu Delingeovy dom\u011Bnky. Konkr\u00E9tn\u00ED c\u00EDle tohoto projektu jsou (1) formulovat a dok\u00E1zat ide\u00E1ln\u00ED homologick\u00E9 perturba\u010Dn\u00ED lemma pro komplexy s netrivi\u00E1ln\u00ED algebraickou strukturou, (2) dok\u00E1zat, \u017Ee siln\u011B homotopick\u00E9 algebry tvo\u0159\u00ED kategorii, a (3) studovat homotopie morfizm\u016F siln\u011B homotopick\u00FDch algeber. Posledn\u00EDm c\u00EDlem bude (4) polo\u017Eit z\u00E1klady teorie rezolvent PROP\u016F popisuj\u00EDc\u00EDch r\u016Fzn\u00E9 typy bialgeber." . . "0"^^ . . . "algebra; topology; mathematical physics; homological perturbation theory; strongly homotopy algebras"@en . . "algebra" . " homological perturbation theory" . "http://www.isvav.cz/projectDetail.do?rowId=IAA1019203"^^ . "The theory of homotopy invariant structures in topology was developed by M. Boardman and R. Vogt in 1973. The first systematic attempt to build up a similar theory for algebraic structures was made much later, in 1999 by the applicant in his paper %22Homotopy algebras are homotopy algebras%22. Some of the methods of the paper have already been succefully applied, for example, in Kontsevich's proof of Deligne s conjecture. Concrete scientific aims of this project are (1) to formulate and prove an idealhomological perturbation lemma for chain complexes with nontrivial algebraic structure, (2) to prove that strongly homotopy algebras from a category and (3) to study homotopies between morphisms of strongly homotopy algebras. The last aim is (4) to outline a theory of resolutions of PROP s describing various types of bialgebras."@en . . . " topology" . . . "2004-10-13+02:00"^^ . . . " mathematical physics" . "Homotopicky invariantn\u00ED struktury v algeb\u0159e" . . "3"^^ . . "0"^^ . .