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Construction par dualité des algèbres de Kac–Moody symétrisables

✍ Scribed by Gilles Halbout

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
142 KB
Volume
222
Category
Article
ISSN
0021-8693

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✦ Synopsis

We know that there is a one to one correspondence between Kac-Moody algebras and generalized Cartan matrices. In Kac ("Infinite-Dimensional Lie algebras," 3rd ed., Cambridge Univ. Press, Cambridge, UK, 1990), one can find a way to reconstruct such an algebra as a Lie algebra presented by generators and relations. The aim of the present work is to give another way to reconstruct those algebras when the Cartan matrix is symmetrisable. Our method will use a semi-classical version of techniques of quantum groups.

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Classification des formes réelles presqu
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✍ Hechmi Ben Messaoud; Guy Rousseau 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 647 KB

Reçu le 5 septembre 2000 Communiqué par J. Tits ## Résumé Real forms of affine Kac-Moody Lie algebras are either almost split or almost compact. Almost split ones have been already classified [J. Algebra 171,. We give here a complete classification of almost compact real forms. Among other result