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Orthogonal symmetric affine Kac-Moody algebras


Author: Walter Freyn
Journal: Trans. Amer. Math. Soc. 367 (2015), 7133-7159
MSC (2010): Primary 17B67, 20G44; Secondary 22E67, 53C35, 17B65
DOI: https://doi.org/10.1090/tran/6257
Published electronically: April 20, 2015
MathSciNet review: 3378826
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Abstract: 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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Walter Freyn
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
Email: freyn@mathematik.tu-darmstadt.de

DOI: https://doi.org/10.1090/tran/6257
Keywords: Lie algebra, affine Kac-Moody algebra, loop algebra, orthogonal symmetric Kac-Moody algebra
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
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.