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SUMMARY:Sophie Emma Mikkelsen (University of Southern Denmark\, Denmark)
DTSTART:20211213T150000Z
DTEND:20211213T160000Z
DTSTAMP:20260422T181000Z
UID:QGS/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/46/">On 
 the quantum symplectic sphere</a>\nby Sophie Emma Mikkelsen (University of
  Southern Denmark\, Denmark) as part of Quantum Groups Seminar [QGS]\n\n\n
 Abstract\nThe algebra of the quantum symplectic $(4n-1)$-sphere $\\mathcal
 {O}(S_q^{4n-1})$ is defined as a subalgebra of the quantum symplectic grou
 p by Faddeev\, Reshetikhin and Takhtajan. Recently D'Andrea and Landi inve
 stigated faithfull irreducible $*$-representations of $\\mathcal{O}(S_q^{4
 n-1})$. They proved that the first $n-1$ generators of its enveloping $C^*
 $-algebra $C(S_q^{4n-1})$ are all zero. The result is a generalisation of 
 the case where $n=2$ which was shown by Mikkelsen and Szymański.\nIn this
  talk\, I will first present how $C(S_q^{4n-1})$ can be described as a gra
 ph $C^*$-algebra\, from which it follows that $C(S_q^{4n-1})$ is isomorphi
 c to the quantum $(2n+1)$-sphere by Vaksman and Soibelman. Then\, I presen
 t a candidate of a vector space basis for $\\mathcal{O}(S_q^{4n-1})$ which
  is constructed by a nontrivial application of the Diamond lemma. The conj
 ecture is supported by computer experiments for $n=1\,...\,8$.  By finding
  a vector space basis we can moreover conclude that the $n-1$ generators a
 re non-zero inside the algebra $\\mathcal{O}(S_q^{4n-1})$.\n
LOCATION:https://researchseminars.org/talk/QGS/46/
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