Simple Restricted Modules for the Restricted Hamiltonian Algebra
نویسندگان
چکیده
منابع مشابه
Simple Restricted Modules for the Restricted Hamiltonian Algebra
The simple restricted modules for the restricted simple Cartan-type Lie algebras fall into two classes. There is a large class consisting of modules induced from simple modules for the subalgebra of nonnegative components. Then there is the small class of exceptional simple modules. Explicit constructions of these exceptional modules and formulas for their dimensions were obtained by Shen [9] f...
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According to [2], the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic p > 7 are either classical or of Cartan type. Lusztig has a conjecture (see [8, p. 294]) which provides a formula for the dimensions of the simple modules for the classical algebras. (In this paper, modules are assumed to be left, finitedimensional and restricted.) Anders...
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It is shown that, with a few exceptions, the simple restricted modules for a restricted contact Lie algebra are induced from those for the homogeneous component of degree zero. In [3], Shen constructed the simple restricted modules for the restricted Witt, special and hamiltonian Lie algebras which comprise three of the four classes of restricted Lie algebras of Cartan type. His methods, howeve...
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The simple modules with homogeneous characters are considered, their dimension formulas are determined.
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Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7172