arXiv subjects

P. Siniscalco

Publications and source records attributed to P. Siniscalco.

3 recordsLinked to original sources

arXiv1998

Explicit Hopf-Galois description of $SL_{e^{2iπ/3}}$-induced Frobenius homomorphisms

The exact sequence of ``coordinate-ring'' Hopf algebras A(SL(2,C)) -> A(SL_q(2)) -> A(F) determined by the Frobenius map Fr, and the same way obtained exact sequence of (quantum) Borel subgroups, are studied when q is a cubic root of unity. An A(SL(2,C))-linear splitting of A(SL_q(2)) making A(SL(2,C)) a direct summand of A(SL_q(2)) is constructed and used to prove that A(SL_q(2)) is a faithfully flat A(F)-Galois extension of A(SL(2,C)). A cocycle and coaction determining the bicrossed-product structure of the upper-triangular (Borel) quantum subgroup of A(SL_q(2)) are computed explicitly.

q-alg↗

arXiv1996

On the Drinfeld Twist for Quantum sl(2)

An isomorphism, up to a twist, between the quasitriangular quantum enveloping algebra U_h(sl(2)) and the (classical) U(sl(2))[[h]]is discussed. The universal twisting element $\cal F$ is given up to the second order in the deformation parameter $h$.

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arXiv1996

Metrics and Pairs of Left and Right Connections on Bimodules

Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an $SL\sb q(2,\IC)$-covariant calculus of the quantum plane plane at a generic $q$ and the cubic root of unity. It is shown that, in the aforementioned examples, giving up the middle-linearity of metrics significantly enlarges the space of metrics. A~metric compatibility condition for the pairs of left and right connections is defined. Also, a compatibility condition between a left and right connection is discussed. Consequences entailed by reducing to the centre of a bimodule the domain of those conditions are investigated in detail. Alternative ways of relating left and right connections are considered.

q-alg↗