Deformations of Quadratic Algebras, the Joseph Ideal for Classical Lie Algebras, and Special Tensors

  • Petr Somberg
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 144)


The Joseph ideal is a unique ideal in the universal enveloping algebra of a simple Lie algebra attached to the minimal coadjoint orbit. Its construction using deformation theory was described by Braverman and Joseph. The same ideal appeared recently in connection with algebra of symmetries of differential operators. The paper presents a review of the corresponding circle of ideas and it discusses a role of special tensors in these questions.


Deformation Theory Coadjoint Orbit Hochschild Cohomology Quadratic Algebra Conformal Killing Vector 
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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Petr Somberg
    • 1
  1. 1.Karlova Universita (Charles University)Czech Republic

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