Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 3 min ago
PreprintCC BY 4.0arXiv

On extensive amenability of algebras

  • Laurent Bartholdi
Open at sourcePDFDOICite

Abstract

For a module M over a cocommutative Hopf algebra π’œ, we define extensive amenability by amenability of its symmetric algebra as a module over Sym(M)#π’œ. Using the author's coalgebraic rounding and quotient theorems, we prove that nonzero extensively amenable modules are amenable, that every module over an amenable Hopf algebra is extensively amenable, and that extensive amenability is preserved and reflected by short exact sequences. For permutation modules this definition agrees, over every field, with extensive amenability of group actions. A final section gives the modifications for exterior algebras and establishes the comparison between the two definitions in several cases.

Related

  1. On amenability of group algebras, I
    Laurent Bartholdi
    Isr. J. Math.Peer-reviewedLicence not statedFull text18 citedAlgebra & number theoryHAL
  2. Equivalence of Pseudo- and Approximate Amenability in Banach Algebras
    Fereidoun Ghahramani, Maedeh Soroushmehr, Yong Zhang
    arXivPreprintCC0Full textAnalysis & PDEsarXiv
  3. Character cyclic amenability of Banach algebras
    Hamid Sadeghi Nahrekhalaji
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Amenability of Lie, Group and Hopf algebras
    Laurent Bartholdi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Amenability via random walks
    Laurent Bartholdi, BΓ‘lint VirΓ‘g
    Duke Mathematical JournalPeer-reviewedLicence not statedFull text136 citedAlgebra & number theoryHAL

Cite

BibTeXRIS
BibTeX
@misc{bartholdi2026extensive,
  title = {{On extensive amenability of algebras}},
  author = {Laurent Bartholdi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00364},
  eprint = {2610.00364},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00364},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On extensive amenability of algebras
AU  - Laurent Bartholdi
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00364
UR  - https://arxiv.org/abs/2610.00364
AB  - For a module M over a cocommutative Hopf algebra π’œ, we define extensive amenability by amenability of its symmetric algebra as a module over Sym(M)#π’œ. Using the author's coalgebraic rounding and quotient theorems, we prove that nonzero extensively amenable modules are amenable, that every module over an amenable Hopf algebra is extensively amenable, and that extensive amenability is preserved and reflected by short exact sequences. For permutation modules this definition agrees, over every field, with extensive amenability of group actions. A final section gives the modifications for exterior algebras and establishes the comparison between the two definitions in several cases.
ER  -