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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Orthogonal symmetric affine Kac-Moody algebras
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by Walter Freyn PDF
Trans. Amer. Math. Soc. 367 (2015), 7133-7159 Request permission


Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues, known as affine Kac-Moody groups. We solve this problem and construct affine Kac-Moody symmetric spaces in a series of several papers. This paper focuses on the algebraic side; more precisely, we introduce OSAKAs, the algebraic structures used to describe the connection between affine Kac-Moody symmetric spaces and affine Kac-Moody algebras and describe their classification.
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Additional Information
  • Walter Freyn
  • Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
  • Email:
  • Received by editor(s): September 6, 2012
  • Received by editor(s) in revised form: May 6, 2013, July 21, 2013, and August 1, 2013
  • Published electronically: April 20, 2015
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7133-7159
  • MSC (2010): Primary 17B67, 20G44; Secondary 22E67, 53C35, 17B65
  • DOI:
  • MathSciNet review: 3378826