A vector space basis of the quantum symplectic sphere

2021/07/03 by Sophie Emma Zegers, Zegers, Sophie Emma
Mathematics · #46L65 #58B34 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2107.01406

openalex publication_date 2021/07/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We present a candidate of a vector space basis for the algebra O(S_q^4n-1) of the quantum symplectic sphere for every n≥ 1. The algebra O(S_q^4n-1) is defined as a certain subalgebra of the quantum symplectic group 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.

Related

• The C^*-algebra of the quantum symplectic sphere
• On quantum quaternion spheres
• Symplectic space and orthogonal space of n qubits
• The R-matrix of the symplecto-orthogonal quantum superalgebra U_q(spo(2n|2m)) in the vector representation
• Canonical bases for quantum generalized Kac-Moody algebra