Noncommutative Ricci Curvature and Dirac Operator on Cq[SL2] at Roots of Unity
نویسندگان
چکیده
منابع مشابه
NONCOMMUTATIVE RICCI CURVATURE AND DIRAC OPERATOR ON Cq[SL2] AT ROOTS OF UNITY
We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group Cq[SL2], 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 D/ and find for q an odd r’th root of unity that its eigenvalues are given by q-integers [m]q for...
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Abstract We compute the noncommutative de Rham cohomology for the finitedimensional q-deformed coordinate ring Cq[SL2] at odd roots of unity and with its standard 4-dimensional differential structure. We find that H1 and H3 have three additional modes beyond the generic q-case where they are 1-dimensional, while H2 has six additional modes. We solve the spin-0 and Maxwell theory on Cq[SL2] incl...
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Abstract. We study Hadamard matrices of order n, formed by l-th roots of unity. A main problem is to find the allowed values of (n, l), and we discuss here the following statement: for l = pa 1 . . . pa s we must have n ∈ p1+. . .+psN. For s = 1 this is a previously known result, for s = 2, 3 this is a result that we prove in this paper, and for s ≥ 4 this is a conjecture that we raise. We pres...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2003
ISSN: 0377-9017
DOI: 10.1023/a:1022980227093