On some commutative subalgebras of the universal enveloping algebra of theLie algebra gl(n,C)

Authors
Tarasov, AA
Citation
Aa. Tarasov, On some commutative subalgebras of the universal enveloping algebra of theLie algebra gl(n,C), SB MATH, 191(9-10), 2000, pp. 1375-1382
Citations number
4
Categorie Soggetti
Mathematics
Journal title
SBORNIK MATHEMATICS
ISSN journal
10645616 → ACNP
Volume
191
Issue
9-10
Year of publication
2000
Pages
1375 - 1382
Database
ISI
SICI code
1064-5616(200009/10)191:9-10<1375:OSCSOT>2.0.ZU;2-
Abstract
For the Lie algebra g = gl(n, C) it is proved that the maximal commutative subalgebras of the Poisson algebra P(g) obtained by the method of shifting the invariants can be lifted to the enveloping algebra. Moreover, this lift ing can be carried out by means of the symmetrization map.