I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 2, PAGES 183-199
Categories of bounded
A. V. Petukhov
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be a reductive Lie algebra
be a reductive in subalgebra.
We call a -module a -module whenever is a direct sum of
We call a -module bounded if there exists
such that for
any simple finite-dimensional -module the dimension of the
component is not more than .
Bounded -modules form a subcategory of the category
a finite-dimensional vector space.
We prove that the categories of bounded -modules and -modules are isomorphic to the
direct sum of countably many copies of the category of representations
of some explicitly described quiver with relations under some mild
assumptions on the dimension of .
Last modified: March 6, 2012