Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 17 min ago
PreprintCC BY 4.0arXiv

General linear and Steinberg groups over the Leavitt algebra L𝔽2(1,2)

  • Huynh Viet Khanh
Open at sourcePDFDOICite

Abstract

Let R=LF2(1,2). We prove that GLr(R) is integrally acyclic for every r≥1 and that the canonical map Str(R)→GLr(R) is an isomorphism for every r≥3. The unit group R× is finitely presented, and we describe an explicit finite presentation. The homology calculation uses leaf coordinates, simultaneous extensions of ordered frames, and finite-field actions on stabilizers. The Steinberg argument lifts relations from a simply connected frame complex and refines coordinates. We also state separate criteria for the two arguments over rings of characteristic two.

Related

  1. Double Steinberg coinvariants for special linear groups
    Tatiana Abdelnaim, David Chan, Alexander Kupers +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  2. Baer-Type Ring Characterizations of Steinberg Algebras, with Applications to Leavitt Path Algebras
    Morteza Ahmadi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  3. The Quillen and sharbly Hopf algebra structures on Steinberg homology coincide
    Urshita Pal, Sam Payne
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  4. When twist of a Leavitt path algebra is again a Leavitt path algebra
    Tran Giang Nam, Ashish K Srivastava
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. The Gaudin model and the super Bethe ansatz for unitarizable modules over the general linear Lie (super)algebra
    Bintao Cao, Wan Keng Cheong, Ngau Lam
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{khanh2026general,
  title = {{General linear and Steinberg groups over the Leavitt algebra $L_\mathbb F_2(1,2)$}},
  author = {Huynh Viet Khanh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08428},
  eprint = {2609.08428},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08428},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - General linear and Steinberg groups over the Leavitt algebra L_𝔽_2(1,2)
AU  - Huynh Viet Khanh
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.08428
UR  - https://arxiv.org/abs/2609.08428
AB  - Let R=L_F_2(1,2). We prove that GL_r(R) is integrally acyclic for every r≥1 and that the canonical map St_r(R)→GL_r(R) is an isomorphism for every r≥3. The unit group R^× is finitely presented, and we describe an explicit finite presentation. The homology calculation uses leaf coordinates, simultaneous extensions of ordered frames, and finite-field actions on stabilizers. The Steinberg argument lifts relations from a simply connected frame complex and refines coordinates. We also state separate criteria for the two arguments over rings of characteristic two.
ER  -