PreprintCC0arXiv
Actions of central Morita monoidal groupoids, and seven term exact sequences of all types
Abstract
We introduce a strict monoidal groupoid associated with a given commutative ring K. It acts on the Clifford extension systems of K-central algebras which are graded by a group G, as well as on the generalized collective characters, both of type ϕ∈ Hom(G, Aut(K)). These actions partition the two sets above with respect to graded Morita equivalence. By that we establish a seven term exact sequence of type ϕ, which boils down to the celebrated Chase-Harrison-Rosenberg sequence when ϕ is Galois.
Related
- Morita equivalence for Lp-operator algebras associated with étale groupoids
- The 2-monoidal structure of symmetric sequences
- Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II
- KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
- Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. I
BibTeX
@misc{antony2026actions,
title = {{Actions of central Morita monoidal groupoids, and seven term exact sequences of all types}},
author = {Ammu Elizabeth Antony and Yuval Ginosar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18101},
eprint = {2610.18101},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18101},
note = {CC0},
}
RIS
TY - UNPB
TI - Actions of central Morita monoidal groupoids, and seven term exact sequences of all types
AU - Ammu Elizabeth Antony
AU - Yuval Ginosar
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18101
UR - https://arxiv.org/abs/2610.18101
AB - We introduce a strict monoidal groupoid associated with a given commutative ring K. It acts on the Clifford extension systems of K-central algebras which are graded by a group G, as well as on the generalized collective characters, both of type ϕ∈ Hom(G, Aut(K)). These actions partition the two sets above with respect to graded Morita equivalence. By that we establish a seven term exact sequence of type ϕ, which boils down to the celebrated Chase-Harrison-Rosenberg sequence when ϕ is Galois.
ER -