Noncommutative Ricci curvature and Dirac operator on $C_q[SL_2]$ at roots of unity

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dc.creatorMajid, Shahn
dc.date2002-06-19
dc.date2002-09-16
dc.date.accessioned2026-07-07T04:49:12Z
dc.date.available2026-07-07T04:49:12Z
dc.descriptionWe find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group $C_q[SL_2]$, using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for $q$ an odd $r$'th root of unity that its eigenvalues are given by $q$-integers $[m]_q$ for $m=0,1,...,r-1$ offset by the constant background curvature. We fully solve the Dirac equation for $r=3$.
dc.description16 pages amslatex. Minor revision to Dirac operator, now solving fully for $r=3$
dc.identifierhttps://arxiv.org/abs/math/0206187
dc.identifierhttp://arxiv.org/abs/math/0206187
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64336
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subject58B32, 58B34
dc.titleNoncommutative Ricci curvature and Dirac operator on $C_q[SL_2]$ at roots of unity
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