PreprintarXiv licencearXiv
On Exceptional CR-Quadrics: Further Developments
Abstract
Exceptional CR-quadrics are studied. An example of an exceptional (4,4)-quadric is constructed; it realizes the minimum exceptional type with respect to both n and k. Its graded Lie algebra is described. The available information on exceptional types is summarized, and the lattice of CR-types is decomposed into the disjoint union of three sets: A, the types for which exceptional quadrics are impossible; B, the types for which examples of exceptional quadrics are known; and C, the types whose status is currently unknown (neither an example nor a nonexistence proof is known). Several questions are posed.
Related
BibTeX
@misc{beloshapka2026exceptional,
title = {{On Exceptional CR-Quadrics: Further Developments}},
author = {V. K. Beloshapka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08501},
eprint = {2609.08501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08501},
}
RIS
TY - UNPB
TI - On Exceptional CR-Quadrics: Further Developments
AU - V. K. Beloshapka
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08501
UR - https://arxiv.org/abs/2609.08501
AB - Exceptional CR-quadrics are studied. An example of an exceptional (4,4)-quadric is constructed; it realizes the minimum exceptional type with respect to both n and k. Its graded Lie algebra is described. The available information on exceptional types is summarized, and the lattice of CR-types is decomposed into the disjoint union of three sets: A, the types for which exceptional quadrics are impossible; B, the types for which examples of exceptional quadrics are known; and C, the types whose status is currently unknown (neither an example nor a nonexistence proof is known). Several questions are posed.
ER -