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arXiv · 2508.18454

On angular momentum algebras and their relations

Kieran Calvert·Marcelo De Martino·Roy Oste
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Abstract

In this paper, we study the centraliser of $\mathfrak{osp}(1|2)$, denoted the total angular momentum algebra (TAMA), in the Weyl Clifford algebra. The TAMA extends the angular momentum algebra (AMA), which arises as the centraliser of $\mathfrak{sl}(2)$ and admits a diagrammatic presentation via the crossing relation described by Feigin and Hakobyan. Using Young symmetrisers we construct an analogue relation for the even subalgebra of the TAMA. We prove that for rank $4$ and $5$ these relations generate a presentation for the even subalgebra of the TAMA.

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Kieran Calvert, Marcelo De Martino, Roy Oste. 2025-08-25. On angular momentum algebras and their relations. https://arxiv.org/abs/2508.18454

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