Warianty tytułu
Abstrakty
An envelope in a category is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or the Stone-Čech compactification of a topological space, or the universal enveloping algebra of a Lie algebra. Dually, a refinement generalizes the operations of "interior enrichment", like bornologification (or saturation) of a locally convex space, or simply connected covering of a Lie group. In this paper we define envelopes and refinements in abstract categories and discuss conditions under which these constructions exist and are functors. The aim of the exposition is to lay the foundations for duality theories of non-commutative groups based on the idea of envelope. The advantage of this approach is that in the arising theories the analogs of group algebras are Hopf algebras. At the same time the classical Fourier and Gelfand transforms are interpreted as envelopes with respect to certain classes of algebras.
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
513
Liczba stron
188
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2016
Twórcy
autor
- Moscow Aviation Institute, (National Research University), Volokolamskoye shosse 4, Moscow, A-80, GSP-3, 125993, Russia
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm702-12-2015
Identyfikatory
DOI
10.4064/dm702-12-2015
Kolekcja
DML-PL
