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Springer INdAM Series

Perspectives in Lie Theory

Editors: Callegaro, F., Carnovale, G., Caselli, F., De Concini, C., De Sole, A. (Eds.)

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About this book

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

About the authors

Filippo Callegaro received his PhD in Mathematics from the Scuola Normale Superiore of Pisa in 2007 under the direction of Mario Salvetti.  In 2008 he took on a teaching position at the Scuola Normale, before moving to the University of Pisa in 2013. His work focuses on the topology of configuration spaces, cohomology of braid groups and generalizations, and hyperplane and toric arrangements.

Giovanna Carnovale received her PhD from the University of Utrecht in 1999 under the direction of Tom Koornwinder. She has held post-doc positions in Cergy-Pontoise, Paris VI, Antwerp, and Rome Tor Vergata. In 2001 she took on a position in Padua, where she has been an associate professor since 2015. Her research interests are in algebra, especially Lie theory, Hopf algebra theory, and representation theory, as well as their the interplay with geometry.

Fabrizio Caselli received his PhD from the Università di Roma La Sapienza in 2003 under the direction of Francesco Brenti. He has held post-doc positions in Lyon and Rome. In 2006 he took on a position in Bologna, where he has been an associate professor since 2014. His main research interests are in algebra and combinatorics, in particular Kazhdan-Luszig theory, Coxeter groups, complex reflection groups and their representations.

Corrado De Concini received his PhD in Mathematics from the University of Warwick in 1975 under the direction of George Lusztig. He has been a professor of mathematics since 1983. Since 1996 he has been a professor at the University of Roma, La Sapienza. He has been a visiting researcher at numerous institutes, including Brandeis University, Mittag Leffler Institute, Tata Institute of Fundamental Research, Harvard University, and MIT. He serves on the editorial boards of Rendiconti Accademia Nazionale dei Lincei, Journal of Transformation Groups, IMRN, Rendiconti di Matematica, Rendiconti del Seminario Matematico-Padova, and Communications in Contemporary Mathematics. In addition, he has made valuable contributions in several areas of algebra and algebraic geometry, including invariant theory, commutative algebra, algebraic and quantic group theory, the Schottky problem, and hyperplane arrangements.

Alberto De Sole received his PhD in Mathematics from the Massachusetts Institute of Technology in 2003 under the supervision of Victor Kac. He has been a B.P. assistant professor at Harvard University’s Department of Mathematics, a researcher at the Department of Mathematics of the University of Rome La Sapienza, and, since 2012, an associate professor at the same University. He has been a visiting researcher at MIT (Boston), IHP (Paris), IHES (Bure sur Yvette, France), and ESI (Vienna). His primary research interests are in algebra, particularly Lie theory, vertex algebras, W-algebras, and their applications, as well as statistical mechanics in physics.

Table of contents (17 chapters)

Table of contents (17 chapters)
  • Introduction to Vertex Algebras, Poisson Vertex Algebras, and Integrable Hamiltonian PDE

    Pages 3-72

    Kac, Victor

  • An Introduction to Algebras of Chiral Differential Operators

    Pages 73-124

    Malikov, Fyodor

  • Representations of Lie Superalgebras

    Pages 125-177

    Serganova, Vera

  • Introduction to W-Algebras and Their Representation Theory

    Pages 179-250

    Arakawa, Tomoyuki

  • Representations of the Framisation of the Temperley–Lieb Algebra

    Pages 253-265

    Chlouveraki, Maria (et al.)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-58971-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-58970-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-3-319-86520-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Perspectives in Lie Theory
Editors
  • Filippo Callegaro
  • Giovanna Carnovale
  • Fabrizio Caselli
  • Corrado De Concini
  • Alberto De Sole
Series Title
Springer INdAM Series
Series Volume
19
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-58971-8
DOI
10.1007/978-3-319-58971-8
Hardcover ISBN
978-3-319-58970-1
Softcover ISBN
978-3-319-86520-1
Series ISSN
2281-518X
Edition Number
1
Number of Pages
X, 461
Number of Illustrations
2783 b/w illustrations, 5 illustrations in colour
Topics