S.E. Zegers
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In this paper, we present a candidate of a vector space basis for the noncommutative algebra O(S
q
4n-1) of the quantum symplectic sphere for every n ≥ 1. The algebra (S
q
4n-1) is defined as a certain subalgebra of the quantum symplectic group O(SP
q(2n)). A nontrivial 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.
...
In this paper, we present a candidate of a vector space basis for the noncommutative algebra O(S q 4n-1) of the quantum symplectic sphere for every n ≥ 1. The algebra (S q 4n-1) is defined as a certain subalgebra of the quantum symplectic group O(SP q(2n)). A nontrivial 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.