The Huang Algebra Ideal and the Diagonal Shift Property
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915937132740608 |
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| author | Addabbo, Darlayne |
| author_facet | Addabbo, Darlayne |
| contents | Let $V$ be a grading-restricted vertex algebra and let $A^\infty(V)=U^\infty(V)/Q^\infty(V)$ be the associative algebra constructed by Huang, where $U^\infty(V)$ is the space of column-finite infinite matrices with entries in V and $Q^\infty(V)$ is an ideal of a (nonassociative) algebra structure on $U^\infty(V)$ defined by Huang. Huang introduced families of elements in $Q^\infty(V)$ and conjectured that these elements generate $Q^\infty(V)$. We discover and prove that Huang's elements all satisfy what we call ``the diagonal shift property". On the other hand, in the case that $V$ is the rank one Heisenberg vertex operator algebra, we construct infinitely many linearly independent elements in $Q^\infty(V)$ that do not satisfy the diagonal shift property. As a corollary, we disprove Huang's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12937 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Huang Algebra Ideal and the Diagonal Shift Property Addabbo, Darlayne Quantum Algebra Let $V$ be a grading-restricted vertex algebra and let $A^\infty(V)=U^\infty(V)/Q^\infty(V)$ be the associative algebra constructed by Huang, where $U^\infty(V)$ is the space of column-finite infinite matrices with entries in V and $Q^\infty(V)$ is an ideal of a (nonassociative) algebra structure on $U^\infty(V)$ defined by Huang. Huang introduced families of elements in $Q^\infty(V)$ and conjectured that these elements generate $Q^\infty(V)$. We discover and prove that Huang's elements all satisfy what we call ``the diagonal shift property". On the other hand, in the case that $V$ is the rank one Heisenberg vertex operator algebra, we construct infinitely many linearly independent elements in $Q^\infty(V)$ that do not satisfy the diagonal shift property. As a corollary, we disprove Huang's conjecture. |
| title | The Huang Algebra Ideal and the Diagonal Shift Property |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2604.12937 |