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arXiv · 2107.01406

A vector space basis of the quantum symplectic sphere

Sophie Emma Zegers
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Abstract

We present a candidate of a vector space basis for the algebra $\mathcal{O}(S_q^{4n-1})$ of the quantum symplectic sphere for every $n\geq 1$. The algebra $\mathcal{O}(S_q^{4n-1})$ is defined as a certain subalgebra of the quantum symplectic group $\mathcal{O}(SP_q(2n))$. A non-trivial application of the Diamond Lemma is used to construct the vector space basis and the conjecture is supported by computer experiments for $n=1,2,...,8$.

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Sophie Emma Zegers. 2021-07-03. A vector space basis of the quantum symplectic sphere. https://arxiv.org/abs/2107.01406

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