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Supports of weight modules over Witt algebras

Published online by Cambridge University Press:  11 February 2011

Volodymyr Mazorchuk  and
Kaiming Zhao
Volodymyr Mazorchuk
Affiliation:
Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden (mazor@math.uu.se)
Kaiming Zhao
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada (kzhao@wlu.ca) and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
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Abstract

As the first step towards a classification of simple weight modules with finite dimensional weight spaces over Witt algebras Wn, we explicitly describe the supports of such modules. We also obtain some descriptions of the support of an arbitrary simple weight module over a ℤn-graded Lie algebra having a root space decomposition with respect to the abelian subalgebra , with the property for all α, β ∈ ℤn, α ≠ β (this class contains the algebra Wn).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 1 , February 2011 , pp. 155 - 170
Copyright
Copyright © Royal Society of Edinburgh 2011

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