| Abstract:
The Gelfand--Kirillov dimension is an important and useful invariant of
infinite dimensional non-commutative algebras and their modules. It has
been used in the past to show that certain \(D\)-modules have finite length and
it proves to be a powerful tool for studying the modules of almost
commutative algebras which include the enveloping algebras of finite
dimensional Lie algebras. in this talk I will discuss the
Gelfand--Kirillov dimension for the irreducible representations of the Weyl
algebra and the quantum torus.
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