PreprintarXiv licencearXiv
On the Fomin-Kirillov algebras
Abstract
The Fomin-Kirillov algebras ā±š¦n are shown to be infinite-dimensional for nā„ 6. By computer calculations, we find an explicit nonzero primitive element of degree 14 in the identity component of ā±š¦6. For every nā„ 6, the existence of such an element implies that ā±š¦n contains a polynomial subalgebra and is therefore infinite-dimensional, and that the canonical homomorphism from ā±š¦n onto its associated Nichols algebra is not an isomorphism.
Related
- Higher Fomin-Kirillov algebras are infinite-dimensional
- Jacobson radical non-nil algebras of Gel'fand-Kirillov dimension 2
- Special Kirillov-Reshetikhin crystals
- Ramified tori and Gelfand--Kirillov dimension of mod p representations
- Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras
BibTeX
@misc{zhang2026fominkirillov,
title = {{On the Fomin-Kirillov algebras}},
author = {Yang Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20033},
eprint = {2610.20033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20033},
}
RIS
TY - UNPB
TI - On the Fomin-Kirillov algebras
AU - Yang Zhang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20033
UR - https://arxiv.org/abs/2610.20033
AB - The Fomin-Kirillov algebras ā±š¦_n are shown to be infinite-dimensional for nā„ 6. By computer calculations, we find an explicit nonzero primitive element of degree 14 in the identity component of ā±š¦_6. For every nā„ 6, the existence of such an element implies that ā±š¦_n contains a polynomial subalgebra and is therefore infinite-dimensional, and that the canonical homomorphism from ā±š¦_n onto its associated Nichols algebra is not an isomorphism.
ER -