Skip to content
DraconiticResearch
Search Sources API
197,787 studies31 sourcesUpdated 1 h ago
PreprintarXiv licencearXiv

Morita equivalent blocks with an endotrivial source that are not globally isotypic

  • Xin Huang
Open at sourcePDFDOICite

Abstract

Let (K,π’ͺ,k) be a large enough $2$-modular system. We construct two nilpotent block algebras of finite groups which are isomorphic as π’ͺ-algebras and are Morita equivalent via a bimodule with an endotrivial source of π’ͺ-rank $3$, but which are not globally isotypic. Hence they are not $2$-permutation equivalent and not splendidly Rickard equivalent. These results separate Morita equivalences with endopermutation source from p-permutation equivalences and splendid Rickard equivalences, and also separate almost global isotypies from global isotypies.

Related

  1. Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations
    Konrad Burnik
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryLogic & foundationsarXiv
  2. Disentangling Measurement Protocol from Material Physics in Isotypic and Anisotypic SiC/Si Heterojunctions: A Metrology-Driven Study for Betavoltaic Energy Conversion
    Mikhail V. Dolgopolov
    arXivPreprintarXiv licenceFull textMathematical physicsApplied physics & instrumentationarXiv
  3. Mumford--Morita--Miller classes in generalised cohomology theories
    Oscar Randal-Williams
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  4. The Morita classes are nonzero
    Alexander Kupers, Jeremy Miller, Peter Patzt
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  5. An Elliptic Path Fibration and Holomorphic Morita Equivalence
    Ahmmadreza Khazaeipoul
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{huang2026morita,
  title = {{Morita equivalent blocks with an endotrivial source that are not globally isotypic}},
  author = {Xin Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.31083},
  eprint = {2608.31083},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.31083},
}
RIS
TY  - UNPB
TI  - Morita equivalent blocks with an endotrivial source that are not globally isotypic
AU  - Xin Huang
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2608.31083
UR  - https://arxiv.org/abs/2608.31083
AB  - Let (K,π’ͺ,k) be a large enough $2$-modular system. We construct two nilpotent block algebras of finite groups which are isomorphic as π’ͺ-algebras and are Morita equivalent via a bimodule with an endotrivial source of π’ͺ-rank $3$, but which are not globally isotypic. Hence they are not $2$-permutation equivalent and not splendidly Rickard equivalent. These results separate Morita equivalences with endopermutation source from p-permutation equivalences and splendid Rickard equivalences, and also separate almost global isotypies from global isotypies.
ER  -