Whittaker Modules for Graded Lie Algebras
نویسنده
چکیده
In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a consequence of this, we obtain a classification of simple Whittaker modules for such algebras. Also, we discuss some concrete algebras as examples.
منابع مشابه
Imaginary Whittaker Modules for Extended Affine Lie Algebras Song Shi a Dissertation Submitted to the Faculty of Graduate Studies in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy Graduate Program in Mathematics and Statistics
We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t̃ obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irredu...
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