Premium
Kostant's Theorem for Special Filtered Algebras
Author(s) -
Futorny Vyacheslav,
Ovsienko Serge
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003844
Subject(s) - mathematics , universal enveloping algebra , algebra over a field , filtered algebra , center (category theory) , lie superalgebra , class (philosophy) , cellular algebra , yangian , pure mathematics , graded lie algebra , lie algebra , algebra representation , affine lie algebra , current algebra , computer science , chemistry , artificial intelligence , crystallography
A famous result of Kostant's states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. An analogue of this result is proved for the class of special filtered algebras. This is then applied to show that the restricted Yangian and the universal enveloping algebra of the restricted current algebra, associated with the general linear Lie algebra, are both free over their centers. 2000 Mathematics Subject Classification 13A02, 16W70, 17B37, 81R10.