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SUMMARY:Satyajit Guin (Indian Institute of Technology Kanpur\, India)
DTSTART:20210614T140000Z
DTEND:20210614T150000Z
DTSTAMP:20260422T175300Z
UID:QGS/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/32/">Equ
 ivariant spectral triple for the compact quantum group $U_q(2)$ for comple
 x deformation parameters</a>\nby Satyajit Guin (Indian Institute of Techno
 logy Kanpur\, India) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract
 \nLet $q=|q|e^{i\\pi\\theta}$ be a nonzero complex number such that $|q|\\
 neq 1$\, and consider the compact quantum group $U_q(2)$. In this talk\, w
 e discuss a complete list of inequivalent irreducible representations of $
 U_q(2)$ and its Peter-Weyl decomposition. Then\, for $\\theta\\notin\\math
 bb{Q}\\setminus\\{0\,1\\}$\, we discuss the $K$-theory of the underlying $
 C^*$-algebra $C(U_q(2))$\, and a spectral triple which is equivariant unde
 r its own comultiplication action. The spectral triple obtained here is ev
 en\, $4^+$-summable\, non-degenerate\, and the Dirac operator acts on two 
 copies of the $L^2$-space of $U_q(2)$. The Chern character of the associat
 ed Fredholm module is nontrivial.\n
LOCATION:https://researchseminars.org/talk/QGS/32/
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