The deformed Lie algebra of differential operators of order at most one. (English) Zbl 1272.13024
Summary: In this paper, we study the algebraic properties of the deformed Lie algebra \(\mathcal{L}\) of differential operators of order at most one. We determine all the derivations, central extensions, and automorphism group of \(\mathcal{L}\). Furthermore, the reducibility criterion for the Verma modules of the universal central extension of \(\mathcal{L}\) is achieved through a study of the Shapovalov form. {
©2011 American Institute of Physics}
©2011 American Institute of Physics}
Keywords:
Shapovalov formReferences:
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