We give a candidate of a vector space basis for the algebra O(S
4n−1
q
) of
the quantum symplectic sphere for every n ≥ 1. The construction follows by a nontrivial application of the Diamond Lemma. The conjecture is supported by computer
experiments for n = 1, 2, ..., 8. The work is motivated by a result of Landi and D’Andrea,
who proved that the first n − 1 generators of the C
∗
-algebra C(S
4n−1
q
), n ≥ 2 are zero.
By finding a vector space basis, we can conclude that these generators are different from
zero in the corresponding algebra O(S
4n−1
q
).
Original language | English |
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Publication date | 3. Jul 2021 |
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Publisher | arXiv |
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Number of pages | 9 |
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Publication status | Published - 3. Jul 2021 |
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