A vector space basis of the quantum symplectic sphere
Sophie Emma Zegers (TU Delft - Electrical Engineering, Mathematics and Computer Science)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
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.