Group graded basic Morita equivalences

Coconet, Tiberiu; Marcus, Andrei

doi:10.1016/j.jalgebra.2017.06.019

Cited by 7 publications

(11 citation statements)

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“…Note that we will only deal with automorphisms of p-groups, and fusions will be regarded as stabilizers of modules under a suitable action. In the end, we prove that these Clifford extensions are preserved by the group graded basic Morita equivalences introduced in [2].…”

Section: Introductionmentioning

confidence: 86%

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Fusions and Clifford extensions

Coconet

Marcus

Todea

2018

Journal of Group Theory

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Section: Introductionmentioning

confidence: 86%

“…In this section we consider basic Morita equivalences between block extensions, as discussed in [2] and Section 1, and we give a proof of the main result of the paper, Theorem 1.2.…”

Section: Graded Basic Morita Equivalences and The Invariance Of Ementioning

confidence: 99%

Fusions and Clifford extensions

Coconet

Marcus

Todea

2018

Journal of Group Theory

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“…2.6. Basic Morita equivalences have been generalized to block extensions in [4]. According to [ In this case, we can again identify…”

Section: 4mentioning

confidence: 99%

“…We treat here these results in the framework of group graded basic Morita equivalences introduced in [4], and further investigated in [5]. To summarize our results, let us introduce some notation.…”

Section: Introductionmentioning

confidence: 99%

Block Extensions, Local Categories and Basic Morita Equivalences

Coconet

Marcus

Todea

2020

The Quarterly Journal of Mathematics

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Let (K , O, k) be a p-modular system with k algebraically closed, let b be a block of the normal subgroup H of G having defect pointed group Q δ in H and P γ in G, and consider the block extension bOG. One may attach to b an extended local category E (b,H,G) , a group extension L of Z(Q) by N G (Q δ )/C H (Q) having P as a Sylow p-subgroup, and a cohomology class [α] ∈ H 2 (N G (Q δ )/QC H (Q), k × ). We prove that these objects are invariant under the G/H-graded basic Morita equivalences introduced in [4]. Along the way, we give alternative proofs of the results of [11] and [23] on extensions of nilpotent blocks, and of [27] on p ′ -extensions of inertial blocks.

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“…The construction is useful for extending to the blocks of the normalizers of the local pointed groups the local equivalences induced by a basic Morita equivalence. The construction was then generalized in [4] to the case of H-interior G-algebras, where H is normal in G. Further remarks and properties are given in [2] and [3] for the case of G/H-graded algebras, serving for the generalization of the main rezult of [5], which was achived in [3].…”

Section: Introductionmentioning

confidence: 99%