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The First Modular Zhu Algebra of L(1/2,0)F in Characteristic Seven
Abstract
Let F be an algebraically closed field of characteristic $7$, and let V=L(1/2,0)F. For the degree-four singular vector q=(L(−2)2−2L(−4))1 in the universal vacuum vertex operator algebra V̅, set Vq=V̅/I(q). We prove that the natural quotient map induces an isomorphism A1(Vq)≅ A1(V)≅ F[T]/(T(T−4)(T−5))≅ F3. Explicit O1(Vq)-relations and four families of triangular PBW straightening relations give the upper bound, while three one-dimensional homogeneous subspaces give the matching lower bound.
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BibTeX
@misc{huang2026first,
title = {{The First Modular Zhu Algebra of $L(\frac12,0)_F$ in Characteristic Seven}},
author = {Haihua Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15448},
eprint = {2610.15448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15448},
}
RIS
TY - UNPB
TI - The First Modular Zhu Algebra of L(1/2,0)_F in Characteristic Seven
AU - Haihua Huang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15448
UR - https://arxiv.org/abs/2610.15448
AB - Let F be an algebraically closed field of characteristic $7$, and let V=L(1/2,0)_F. For the degree-four singular vector q=(L(−2)^2−2L(−4))1 in the universal vacuum vertex operator algebra V̅, set V_q=V̅/I(q). We prove that the natural quotient map induces an isomorphism A_1(V_q)≅ A_1(V)≅ F[T]/(T(T−4)(T−5))≅ F^3. Explicit O_1(V_q)-relations and four families of triangular PBW straightening relations give the upper bound, while three one-dimensional homogeneous subspaces give the matching lower bound.
ER -