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Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants

  • Dmitri I. PanyushevEmail author
  • Oksana S. Yakimova
Chapter
Part of the Progress in Mathematics book series (PM, volume 330)

Abstract

This is a part of an ongoing project, the goal of which is to classify all semi-direct products \({\mathfrak {s}}={\mathfrak g}{\ltimes }V\) such that \({\mathfrak g}\) is a simple Lie algebra, V  is a \({\mathfrak g}\)-module, and \({\mathfrak {s}}\) has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras.

Keywords

Classical Lie algebras Coadjoint representation Symmetric invariants 

MSC

17B63 14L30 17B20 22E46 

Notes

Acknowledgements

The first author is partially supported by the RFBR grant Open image in new window 16-01-00818. The second author is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number 330450448.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems of the R.A.SMoscowRussia
  2. 2.Universität zu Köln Mathematisches InstitutKölnDeutschland

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