Poincaré duality for $k$-$A$ Lie superalgebras

Chemla, Sophie

doi:10.24033/bsmf.2238

Cited by 16 publications

(32 citation statements)

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“…Proposition 7.4 is proved in full generality in the context of Lie superalgebras in [Chemla 1994]. The proof in the present case is very similar to that of [Chemla 2004, Corollary 3.2.5].…”

Section: Applicationssupporting

confidence: 60%

“…Proposition 7.4 is proved in full generality in the context of Lie superalgebras in [Chemla 1994]. This result has already been obtained in [Dolgushev and Etingof 2005] for a deformation of the algebra of regular functions on a smooth algebraic affine variety.…”

Section: Introductionmentioning

confidence: 75%

“…The character defined by the right action of Chemla 1994]. Thus, the character defined by Theorem 4.1 is a quantization of the character trad g .…”

Section: Notation We Denote Bymentioning

confidence: 99%

“…We now extend to Hopf algebras another duality property for induced representations of Lie algebras [Chemla 1994]. …”

Section: Applicationsmentioning

confidence: 99%

“…In this case, d = dim g and the character defined by the right representation of U (g) on Ext dim g U (g) (k, U (g)) is Trad g [Chemla 1994]. The algebra of regular functions on an affine algebraic Poisson group and the algebra of formal power series also satisfy these hypothesis.…”

Section: Introductionmentioning

confidence: 99%

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Duality properties for quantum groups

Chemla¹

2011

Pacific J. Math.

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Some duality properties for induced representations of enveloping algebras involve the character Trad g . We extend them to deformation Hopf algebras A h of a noetherian Hopf k-algebra A 0 satisfying Extwhere it is isomorphic to k. These duality properties involve the character of A h defined by right multiplication on the one-dimensional freeIn the case of quantized enveloping algebras, this character lifts the character Trad g . We also prove Poincaré duality for such deformation Hopf algebras in the case where k [[h]] is an A h -module of finite projective dimension. We explain the relation of our construction with quantum duality.

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“…Proposition 7.4 is proved in full generality in the context of Lie superalgebras in [Chemla 1994]. The proof in the present case is very similar to that of [Chemla 2004, Corollary 3.2.5].…”

Section: Applicationssupporting

confidence: 60%

Section: Introductionmentioning

confidence: 75%

“…The character defined by the right action of Chemla 1994]. Thus, the character defined by Theorem 4.1 is a quantization of the character trad g .…”

Section: Notation We Denote Bymentioning

confidence: 99%

“…We now extend to Hopf algebras another duality property for induced representations of Lie algebras [Chemla 1994]. …”

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%