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- W2963442659 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 $Ext^{i}_{A_{0}}(k, A_{0})={0}$ 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 $Ext^{d}_{A_{h}} (k[[h]], A_{h})$. In the case of quantized enveloping algebras, this character lifts the character $Trad_{goth g}$. We also prove Poincar{'e} 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." @default.
- W2963442659 created "2019-07-30" @default.
- W2963442659 creator A5035329039 @default.
- W2963442659 date "2011-10-29" @default.
- W2963442659 modified "2023-09-25" @default.
- W2963442659 title "Duality properties for quantum groups" @default.
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- W2963442659 doi "https://doi.org/10.2140/pjm.2011.252.313" @default.
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