Cohomology Of Infinite-dimensional Lie Algebras (monographs In Contemporary Mathematics)
by D.B. Fuks /
1986 / English / DjVu
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There is no question that the cohomology of infinite dimensional
Lie algebras deserves a brief and separate mono graph. This
subject is not cover~d by any of the tradition al branches of
mathematics and is characterized by relative ly elementary proofs
and varied application. Moreover, the subject matter is widely
scattered in various research papers or exists only in verbal form.
The theory of infinite-dimensional Lie algebras differs markedly
from the theory of finite-dimensional Lie algebras in that the
latter possesses powerful classification theo rems, which usually
allow one to "recognize" any finite dimensional Lie algebra (over
the field of complex or real numbers), i.e., find it in some list.
There are classifica tion theorems in the theory of
infinite-dimensional Lie al gebras as well, but they are
encumbered by strong restric tions of a technical character. These
theorems are useful mainly because they yield a considerable supply
of interest ing examples. We begin with a list of such examples,
and further direct our main efforts to their study.
There is no question that the cohomology of infinite dimensional
Lie algebras deserves a brief and separate mono graph. This
subject is not cover~d by any of the tradition al branches of
mathematics and is characterized by relative ly elementary proofs
and varied application. Moreover, the subject matter is widely
scattered in various research papers or exists only in verbal form.
The theory of infinite-dimensional Lie algebras differs markedly
from the theory of finite-dimensional Lie algebras in that the
latter possesses powerful classification theo rems, which usually
allow one to "recognize" any finite dimensional Lie algebra (over
the field of complex or real numbers), i.e., find it in some list.
There are classifica tion theorems in the theory of
infinite-dimensional Lie al gebras as well, but they are
encumbered by strong restric tions of a technical character. These
theorems are useful mainly because they yield a considerable supply
of interest ing examples. We begin with a list of such examples,
and further direct our main efforts to their study.