On the representation theory of the Drinfeld double of the Fomin-Kirillov algebra $\mathcal{FK}_3$

Pogorelsky, Barbara; Vay, Cristian

doi:10.48550/arxiv.1707.02091

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2017

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“…(vi) follows from Lemma 2.6 (i) and (27). The remaining items are deduced from (i) and Lemma 2.6 (iii).…”

Section: Graded Modulesmentioning

confidence: 91%

“…• ch P(e, ρ) = ch M(τ, 0) = ch M(τ, 0) + ch M(e, ρ) + ch M(σ, −). Together with Barbara Pogorelsky, we study these projective modules more in detail [27]. We also discuss the tensor product between the simple and projective modules.…”

Section: 3mentioning

confidence: 99%

“…Moreover, we can infer the tensor product between simple and projective modules from the multiplication of their graded characters in the ring ZΛ[t, t −1 ]. We carry out this plan for B(V ) = F K 3 and G = S 3 jointly with Barbara Pogorelsky in [27].…”

Section: Introductionmentioning

confidence: 99%

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On Projective Modules Over Finite Quantum Groups

Vay

2017

Transformation Groups

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Abstract. Let D be the Drinfeld double of the bosonization B(V )#kG of a finite-dimensional Nichols algebra B(V ) over a finite group G. It is known that the simple D-modules are parametrized by the simple modules over D(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple D(G)-module λ.In the present work, we show that the projective D-modules are filtered by Verma modules and the BGG Reciprocity [P(µ) :holds for the projective cover P(µ) of L(µ). We use graded characters to proof the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.

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“…(vi) follows from Lemma 2.6 (i) and (27). The remaining items are deduced from (i) and Lemma 2.6 (iii).…”

Section: Graded Modulesmentioning

confidence: 91%

Section: 3mentioning

confidence: 99%