Generalized Lie Theory in Mathematics, Physics and Beyond

  • Sergei Silvestrov
  • Eugen Paal
  • Viktor Abramov
  • Alexander Stolin

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Non-Associative and Non-Commutative Structures for Physics

    1. Aristophanes Dimakis, Folkert Müller-Hoissen
      Pages 9-27
    2. Chris Athorne
      Pages 29-37
    3. Lars Hellström
      Pages 47-67
  3. Non-Commutative Deformations, Quantization, Homological Methods, and Representations

  4. Groups and Actions

    1. Eugen Paal, Jüri Virkepu
      Pages 131-140
    2. Tatjana Gramushnjak, Peeter Puusemp
      Pages 151-159
    3. Maido Rahula, Vitali Retšnoi
      Pages 161-170
  5. Quasi-Lie, Super-Lie, Hom-Hopf and Super-Hopf Structures and Extensions, Deformations and Generalizations of Infinite-Dimensional Lie Algebras

    1. Abdenacer Makhlouf, Sergei Silvestrov
      Pages 189-206
    2. K. Kanakoglou, C. Daskaloyannis
      Pages 207-218
    3. Gunnar Sigurdsson, Sergei Silvestrov
      Pages 247-255
  6. Commutative Subalgebras in Noncommutative Algebras

    1. Sergei Silvestrov, Christian Svensson, Marcel de Jeu
      Pages 265-280
    2. Johan Öinert, Sergei D. Silvestrov
      Pages 281-296
    3. Čestmír Burdík, Ondřej Navrátil
      Pages 297-302
  7. Back Matter
    Pages 303-305

About this book


The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.
This volume is devoted to the interplay between several rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.
The book will be a useful source of inspiration for a broad spectrum of researchers and for research students, and includes contributions from several large research communities in modern mathematics and physics.
This volume consists of 5 parts comprising 25 chapters, which were contributed by 32 researchers from 12 different countries. All contributions in the volume have been refereed.


Algebra Integrable systems algebras groups Non-associative algebras Quasi Lie algebras linear algebra

Editors and affiliations

  • Sergei Silvestrov
    • 1
  • Eugen Paal
    • 2
  • Viktor Abramov
    • 3
  • Alexander Stolin
    • 4
  1. 1.Centre for Mathematical Sciences, Division of MathematicsLund Institute of Technology, Lund UniversityLundSweden
  2. 2.Department of MathematicsTallinn University of TechnologyTallinnEstonia
  3. 3.Institute of Pure MathematicsUniversity of TartuTartuEstonia
  4. 4.Department of Mathematical SciencesMathematical Sciences Chalmers University of Technology and Göteborg UniversityGöteborgSweden

Bibliographic information

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