Originating from graduate topics courses given by the first author,
this book functions as a unique text-monograph hybrid that bridges
a traditional graduate course to research level representation
theory. The exposition includes an introduction to the subject,
some highlights of the theory and recent results in the field, and
is therefore appropriate for advanced graduate students entering
the field as well as research mathematicians wishing to expand
their knowledge. The mathematical background required varies from
chapter to chapter, but a standard course on Lie algebras and their
representations, along with some knowledge of homological algebra,
is necessary. Basic algebraic geometry and sheaf cohomology are
needed for Chapter 10. Exercises of various levels of difficulty
are interlaced throughout the text to add depth to topical
comprehension. The unifying theme of this book is the structure and
representation theory of infinite-dimensional locally reductive Lie
algebras and superalgebras. Chapters 1-6 are foundational; each of
the last 4 chapters presents a self-contained study of a
specialized topic within the larger field. Lie superalgebras and
flag supermanifolds are discussed in Chapters 3, 7, and 10, and may
be skipped by the reader.
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