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Unconventional Lie Algebras
Edited by: Dmitry Fuchs
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Advances in Soviet Mathematics
1993; 216 pp; hardcover
Volume: 17
ISBN-10: 0-8218-4121-1
ISBN-13: 978-0-8218-4121-1
List Price: US$128
Member Price: US$102.40
Order Code: ADVSOV/17
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This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinite-dimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups. Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of Kac-Moody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields. The paper by Retakh and Shander contains a generalization of the Schwarz derivative to the noncommutative case.

Readership

Research mathematicians.

Table of Contents

  • A. B. Astashkevich and D. B. Fuchs -- On the cohomology of the Lie superalgebra \(W(m\vert n)\)
  • B. Feigin and F. Malikov -- Integral intertwining operators and complex powers of differential and \(q\)-difference operators
  • D. Fuchs -- Singular vectors over the Virasoro algebra and extended Verma modules
  • K. V. Kozerenko -- Main theorems of invariant theory for the Lie algebra \(\mathfrak{sl}(2)\) in the case of a field of finite characteristic
  • F. Malikov -- On a duality for \({\mathbb Z}\)-graded algebras and modules
  • V. Yu. Ovsienko and O. D. Ovsienko -- Projective structures and infinite-dimensional Lie algebras associated with a contact manifold
  • V. S. Retakh and V. N. Shander -- The Schwarz derivative for noncommutative differential algebras
  • F. V. Weinstein -- Filtering bases: A tool to compute cohomologies of abstract subalgebras of the Witt algebra
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