Duality properties for quantum groups

Abstract

Some duality properties for induced representations of enveloping algebras involve the character $Trad_{\goth g}$. We extend them to deformation Hopf algebras $A_h$ of a noetherian Hopf $k$-algebra $A_0$ satistying $Ex{t}_{A_0}^i(k,A_0)=\{0\}$ except for $i=d$ where it is isomorphic to $k$. These duality properties involve the character of $A_h$ defined by right multiplication on the one dimensional free $k[[h]]$-module $Ex{t}_{A_h}^d(k[[h]],A_h)$. In the case of quantized enveloping algebras, this character lifts the character $Trad_{\goth g}$. We also prove Poincar{é} duality for such deformation Hopf algebras in the case where $A_0$ is of finite homological dimension. We explain the relation of our construction with quantum duality.

38 pages

Cited by in corpus (1)

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