Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
PreprintarXiv licencearXiv

Graded bimodules over split group algebras: stabilizers and Peirce decompositions

  • Felipe de Mattos Chafik Hindi
  • Waldeck Schutzer
Open at sourcePDFDOICite

Abstract

We classify, up to graded isomorphism, graded bimodules over split group algebras of finite abelian subgroups of an arbitrary group. The classification is governed by double cosets, stabilizer characters, and coefficient modules. Over a field, we determine the essential image of the induction functor on Yetter-Drinfel'd modules, giving a negative answer to a question of Dos Santos and Yasumura in the nonabelian case. We also compute the Peirce components and characterize multiplicity-free bimodules through extensions of stabilizer characters.

Related

  1. Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic
    Dong Liu, Yufeng Pei, Limeng Xia
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv
  2. Commutative algebras satisfying univariate identities with vanishing Peirce polynomial
    Daniel J. F. Fox, Vladimir G. Tkachev
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. On the Peirce spectral rigidity of decorated incidence algebras
    Daniel J. F. Fox, Vladimir G. Tkachev
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Simplicity and pure infiniteness for C*-algebras associated with stabilizers of boundary actions
    Felipe Flores, Joseph Gondek
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  5. Cotensor decompositions for comodules over graded vertex operator coalgebras
    Hao Wang
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{hindi2026graded,
  title = {{Graded bimodules over split group algebras: stabilizers and Peirce decompositions}},
  author = {Felipe de Mattos Chafik Hindi and Waldeck Schutzer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06072},
  eprint = {2610.06072},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06072},
}
RIS
TY  - UNPB
TI  - Graded bimodules over split group algebras: stabilizers and Peirce decompositions
AU  - Felipe de Mattos Chafik Hindi
AU  - Waldeck Schutzer
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06072
UR  - https://arxiv.org/abs/2610.06072
AB  - We classify, up to graded isomorphism, graded bimodules over split group algebras of finite abelian subgroups of an arbitrary group. The classification is governed by double cosets, stabilizer characters, and coefficient modules. Over a field, we determine the essential image of the induction functor on Yetter-Drinfel'd modules, giving a negative answer to a question of Dos Santos and Yasumura in the nonabelian case. We also compute the Peirce components and characterize multiplicity-free bimodules through extensions of stabilizer characters.
ER  -