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An explicit product for the on-shell higher-spin algebra in AdSd-space
Abstract
For d>3 we construct the product of the bosonic on-shell higher-spin algebra directly on the AdS-traceless representatives. We find the traceless projector in closed form, determine all linear relations among the trace-producing operators, and prove that every class modulo the sp(2) ideal has a unique traceless representative. The resulting product is an explicit differential operator, which we test on the so(d−1,2) generators. A toy model shows how the factorisation lifts from bilinear products to trilinear ones in minimal A∞-algebras.
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BibTeX
@misc{povarnin2026explicit,
title = {{An explicit product for the on-shell higher-spin algebra in $AdS_d$-space}},
author = {M. A. Povarnin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26704},
eprint = {2610.26704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26704},
}
RIS
TY - UNPB
TI - An explicit product for the on-shell higher-spin algebra in AdS_d-space
AU - M. A. Povarnin
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26704
UR - https://arxiv.org/abs/2610.26704
AB - For d>3 we construct the product of the bosonic on-shell higher-spin algebra directly on the AdS-traceless representatives. We find the traceless projector in closed form, determine all linear relations among the trace-producing operators, and prove that every class modulo the sp(2) ideal has a unique traceless representative. The resulting product is an explicit differential operator, which we test on the so(d−1,2) generators. A toy model shows how the factorisation lifts from bilinear products to trilinear ones in minimal A_∞-algebras.
ER -