In algebra, an integrable module (or integrable representation) of a
Kac–Moody algebra
In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a g ...
(a certain
infinite-dimensional Lie algebra) is a
representation
Representation may refer to:
Law and politics
*Representation (politics), political activities undertaken by elected representatives, as well as other theories
** Representative democracy, type of democracy in which elected officials represent a ...
of
such that (1) it is a sum of weight spaces and (2) the Chevalley generators
of
are
locally nilpotent. For example, the
adjoint representation
In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is \m ...
of a Kac–Moody algebra is
integrable.
Notes
References
*
Abstract algebra
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