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Kac–Moody algebras and Lie algebras of regular vector fields on tori

✍ Scribed by M. Rausch de Traubenberg; M.J. Slupinski

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
159 KB
Volume
253
Category
Article
ISSN
0021-8693

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✦ Synopsis

We consider the problem of representing the Kac-Moody algebra g(N) specified by an r × r indecomposable generalized Cartan matrix N as vector fields on the torus C * r . It is shown that, if the representations are of a certain form, this is possible if and only if g(N) is isomorphic to either sl(r + 1, C) or sl(r, C). For sl(r + 1, C) and sl(r, C), discrete families of representations are constructed. These generalize the well-known discrete families of representations of sl(2, C) as regular vector fields on C * .

📜 SIMILAR VOLUMES

Nilpotent Lie Algebras of Maximal Rank a
Nilpotent Lie Algebras of Maximal Rank and of Kac–Moody Type: E6(1)
✍ D. Fernández-Ternero; J. Núñez-Valdés 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 271 KB

The first family of Kac-Moody Lie algebras studied are the simple Lie algebras. The study of nilpotent Lie algebras of maximal rank and of type A B C D was made by Favre and Santharoubane in [5]. Later, Agrafiotou and Tsagas studied these algebras, of types E 6 E 7 , and E 8 finding that there exist