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Generalized Lie Theory in Mathematics, Physics and Beyond

  • Book
  • © 2009

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Editors:
  1. Sergei Silvestrov

    1. Centre for Mathematical Sciences, Division of Mathematics, Lund Institute of Technology, Lund University, Lund, Sweden

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  2. Eugen Paal

    1. Department of Mathematics, Tallinn University of Technology, Tallinn, Estonia

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  3. Viktor Abramov

    1. Institute of Pure Mathematics, University of Tartu, Tartu, Estonia

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  4. Alexander Stolin

    1. Department of Mathematical Sciences, Mathematical Sciences Chalmers University of Technology and Göteborg University, Göteborg, Sweden

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  • Cutting edge content in Lie theory

  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

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

    1. Moufang Transformations and Noether Currents

      • Eugen Paal
      Pages 3-8

    2. Weakly Nonassociative Algebras, Riccati and KP Hierarchies

      • Aristophanes Dimakis, Folkert Müller-Hoissen
      Pages 9-27

    3. Applications of Transvectants

      • Chris Athorne
      Pages 29-37

    4. Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics

      • Artur E. Ruuge, Fred Van Oystaeyen
      Pages 39-45

    5. A Rewriting Approach to Graph Invariants

      • Lars Hellström
      Pages 47-67

  3. Non-Commutative Deformations, Quantization, Homological Methods, and Representations

    1. Graded q-Differential Algebra Approach to q-Connection

      • Viktor Abramov
      Pages 71-79

    2. On Generalized N-Complexes Coming from Twisted Derivations

      • Daniel Larsson, Sergei D. Silvestrov
      Pages 81-88

    3. Remarks on Quantizations, Words and R-Matrices

      • Hilja L. Huru
      Pages 89-98

    4. Connections on Modules over Singularities of Finite and Tame CM Representation Type

      • Eivind Eriksen, Trond Stølen Gustavsen
      Pages 99-108

    5. Computing Noncommutative Global Deformations Of D-Modules

      • Eivind Eriksen
      Pages 109-117

    6. Comparing Small Orthogonal Classes

      • G. D'Este
      Pages 119-128

  4. Groups and Actions

    1. How to Compose Lagrangian?

      • Eugen Paal, Jüri Virkepu
      Pages 131-140

    2. Semidirect Products of Generalized Quaternion Groups by a Cyclic Group

      • Peeter Puusemp
      Pages 141-149

    3. A Characterization Of A Class Of 2-Groups By Their Endomorphism Semigroups

      • Tatjana Gramushnjak, Peeter Puusemp
      Pages 151-159

    4. Adjoint Representations and Movements

      • Maido Rahula, Vitali Retšnoi
      Pages 161-170

    5. Applications of Hypocontinuous Bilinear Maps in Infinite-Dimensional Differential Calculus

      • Helge Glöckner
      Pages 171-186

  5. Quasi-Lie, Super-Lie, Hom-Hopf and Super-Hopf Structures and Extensions, Deformations and Generalizations of Infinite-Dimensional Lie Algebras

    1. Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras

      • Abdenacer Makhlouf, Sergei Silvestrov
      Pages 189-206

    2. Bosonisation and Parastatistics

      • K. Kanakoglou, C. Daskaloyannis
      Pages 207-218

    3. Deformations of the Witt, Virasoro, and Current Algebra

      • M. Schlichenmaier
      Pages 219-234
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Keywords

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.

Editors and Affiliations

  • Centre for Mathematical Sciences, Division of Mathematics, Lund Institute of Technology, Lund University, Lund, Sweden

    Sergei Silvestrov

  • Department of Mathematics, Tallinn University of Technology, Tallinn, Estonia

    Eugen Paal

  • Institute of Pure Mathematics, University of Tartu, Tartu, Estonia

    Viktor Abramov

  • Department of Mathematical Sciences, Mathematical Sciences Chalmers University of Technology and Göteborg University, Göteborg, Sweden

    Alexander Stolin

Bibliographic Information

  • Book Title: Generalized Lie Theory in Mathematics, Physics and Beyond

  • Editors: Sergei Silvestrov, Eugen Paal, Viktor Abramov, Alexander Stolin

  • DOI: https://doi.org/10.1007/978-3-540-85332-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Hardcover ISBN: 978-3-540-85331-2Published: 12 November 2008

  • Softcover ISBN: 978-3-642-09904-5Published: 19 October 2010

  • eBook ISBN: 978-3-540-85332-9Published: 18 November 2008

  • Edition Number: 1

  • Number of Pages: XVIII, 306

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Algebra, Topological Groups, Lie Groups, Theoretical, Mathematical and Computational Physics

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