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SUMMARY:Satyajit Guin (IIT Kanpur)
DTSTART:20210622T120000Z
DTEND:20210622T130000Z
DTSTAMP:20260423T010753Z
UID:MatPhySem/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MatPhySem/6/
 ">Equivariant spectral triple for the compact quantum group $U_q(2)$ for c
 omplex deformation parameters</a>\nby Satyajit Guin (IIT Kanpur) as part o
 f Mathematical Physics Seminar\n\n\nAbstract\nLet $q=|q|e^{i\\pi\\theta}$ 
 be a nonzero complex number such that $|q|\\neq 1$\, and consider the comp
 act quantum group $U_q(2)$. In this talk\, we discuss a complete list of i
 nequivalent irreducible representations of $U_q(2)$ and its Peter-Weyl dec
 omposition. Then\, for $\\theta\\notin\\mathbb{Q}\\setminus\\{0\,1\\}$ we 
 discuss the $K$-theory of the underlying $C^*$-algebra $C(U_q(2))$\, and a
  spectral triple which is equivariant under the comultiplication action of
  $U_q(2)$. The spectral triple obtained here is even\, $4^+$-summable\, no
 n-degenerate\, and the Dirac operator acts on two copies of the $L^2$-spac
 e of $U_q(2)$. The Chern character of the associated Fredholm module is no
 ntrivial.\n\nThis is a joint work with Bipul Saurabh.\n
LOCATION:https://researchseminars.org/talk/MatPhySem/6/
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