Naslov
On noncommutative Noetherian schemes

Autori
Širola, Boris

Izvornik
Journal of Algebra (0021-8693) 282 (2004), 2; 667-698

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Noetherian ring; Ore set; localization; Artin-Rees property; Zariski topology; prime spectrum; classical structure sheaf; weakly normal element

Sažetak
The main aim of this paper is to better understand the localization technique for certain Noetherian rings like enveloping algebras of nilpotent Lie algebras. For such rings R we also give a conjectural definition of certain sheaves which should be 'affine' objects naturally generalizing the classically defined structure sheaves in commutative theory. The corresponding sheaves associated to some R-modules might carry particularly interesting information ; e.g., for representation theory of semisimple Lie groups. Next, we generalize one important theorem of P. F. Smith on localization in Noetherian Artin-Rees rings. As an interesting corollary we obtain that every prime ideal of height 1 in the enveloping algebra of the Lie algebra sl(2) over a field of characteristic zero is localizable. Finally, we provide a number of concrete useful calculations for our main example, the enveloping algebra of the three-dimensional Heisenberg Lie algebra ; and thus test both the proposed ideas and methods. In particular, we introduce the notion of a weakly normal element, generalizing the notion of a normal element.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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