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Verma type module over an extended affine TKK algebra.
Full text
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| Author(s): |
Anliy Natsuyo Nashimoto Sargeant
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2007-03-30 |
| Examining board members: |
Vyacheslav Futorny;
Ivan Chestakov;
Marinês Guerreiro;
Plamen Emilov Kochloukov;
Adriano Adrega de Moura
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| Advisor: | Vyacheslav Futorny |
| Abstract | |
The extended affine TKK Lie algebras belong to a class of Lie algebras called extended affine Lie algebras of type $A_1$. They are obtained from a semilattice on $\\mathbbR^n$. We studied the structure of the Verma type modules for the extended affine TKK algebra obtained from a semi-lattice (non-lattice) on $\\mathbbR^2$. Fixing a set of positive isotropic roots called standard we found four orbits of the Borel subalgebra each of which give distinct Verma modules for the extended affine TKK algebra. We studied the structures of their submodules and found a criteria for irreducibility for the classic and imaginary Verma modules. (AU) | |