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Pavel Pyatov - One of the best experts on this subject based on the ideXlab platform.
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spectral extension of the quantum group Cotangent Bundle
Communications in Mathematical Physics, 2009Co-Authors: A P Isaev, Pavel PyatovAbstract:The structure of a Cotangent Bundle is investigated for quantum linear groups GL q (n) and SL q (n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SL q (n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators—the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SL q (n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of the q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. The relation between the two operators is given by a modular functional equation for the Riemann theta function.
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spectral extension of the quantum group Cotangent Bundle
arXiv: Quantum Algebra, 2008Co-Authors: A P Isaev, Pavel PyatovAbstract:The structure of a Cotangent Bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.
D. D. Porosniuc - One of the best experts on this subject based on the ideXlab platform.
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a class of locally symmetric kahler einstein structures on the nonzero Cotangent Bundle of a space form
Balkan Journal of Geometry and its Applications (BJGA), 2004Co-Authors: D. D. PorosniucAbstract:We obtain a class of locally symetric Kahler Einstein structures on the nonzero Cotangent Bundle of a Riemannian manifold of positive constant sec- tional curvature. The obtained class of Kahler Einstein structures depends on one essential parameter and cannot have constant holomorphic sectional curva- ture.
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A locally symmetric Kahler Einstein structure on the Cotangent Bundle of a space form
2004Co-Authors: D. D. PorosniucAbstract:We obtain a locally symmetric Kahler Einstein structure on the Cotangent Bundle of a Riemannian manifold of negative constant sectional curvature. Simi- lar results are obtained on a tube around zero section in the Cotangent Bundle, in the case of a Riemannian manifold of positive constant sectional curvature. The obtained Kahler Einstein structures cannot have constant holomorphic sectional curvature.
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a locally symmetric kaehler einstein structure on a tube in the nonzero Cotangent Bundle of a space form
arXiv: Differential Geometry, 2003Co-Authors: D. D. PorosniucAbstract:We obtain a locally symmetric Kaehler Einstein structure on a tube in the nonzero Cotangent Bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature.
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A locally symmetric Kaehler Einstein structure on the Cotangent Bundle of a space form
arXiv: Differential Geometry, 2003Co-Authors: D. D. PorosniucAbstract:We obtain a locally symmetric Kaehler Einstein structure on the Cotangent Bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the Cotangent Bundle, in the case of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structures cannot have constant holomorphic sectional curvature.
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a kaehler einstein structure on the Cotangent Bundle of a riemannian manifold
arXiv: Differential Geometry, 2003Co-Authors: Vasile Oproiu, D. D. PorosniucAbstract:We use the natural lifts of the fundamental tensor field g to the Cotangent Bundle T*M of a Riemannian manifold (M,g), in order to construct an almost Hermitian structure (G,J) of diagonal type on T*M. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and the second coefficient, involved in its definition is expressed as a rational function of the first coefficient and its first order derivative. Next one shows that the obtained almost Hermitian structure is almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian structures on T*M, depending on one essential parameter. Next we study the conditions under which the considered Kaehlerian structure is Einstein. In this case (T*M,G,J) has constant holomorphic curvature.
Filip Blaschke - One of the best experts on this subject based on the ideXlab platform.
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Cotangent Bundle over hermitian symmetric space e 7 e 6 u 1 from projective superspace
Journal of High Energy Physics, 2013Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\mathcal{N}=2$ supersymmetric sigma model on the Cotangent Bundle over the Hermitian symmetric space E 7 /(E 6 × U(1)) in the projective superspace formalism, which is a manifest $\mathcal{N}=2$ off-shell superfield formulation in four-dimensional spacetime. To obtain this model we elaborate on the results developed in arXiv:0811.0218 and present a new closed formula for the Cotangent Bundle action, which is valid for all Hermitian symmetric spaces. We show that the structure of the Cotangent Bundle action is closely related to the analytic structure of the Kahler potential with respect to a uniform rescaling of coordinates.
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Cotangent Bundle over hermitian symmetric space e_7 e_6 times u 1 from projective superspace
arXiv: High Energy Physics - Theory, 2012Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\cN=2$ supersymmetric sigma model on the Cotangent Bundle over the Hermitian symmetric space $E_7/(E_6\times U(1))$ in the projective superspace formalism, which is a manifest $\cN=2$ off-shell superfield formulation in four-dimensional spacetime. To obtain this model we elaborate on results developed in arXiv:0811.0218 and present a new closed formula for the Cotangent Bundle action, which is valid for all Hermitian symmetric spaces. We show that the structure of Cotangent Bundle action is intimately related to the analytic structure of the K\"ahler potential with respect to a uniform rescaling of coordinates.
Mark J. Gotay - One of the best experts on this subject based on the ideXlab platform.
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On symplectic submanifolds of Cotangent Bundles
Letters in Mathematical Physics, 1993Co-Authors: Mark J. GotayAbstract:Necessary and sufficient conditions are given for a symplectic submanifold of a Cotangent Bundle to itself be a Cotangent Bundle.
Masato Arai - One of the best experts on this subject based on the ideXlab platform.
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Cotangent Bundle over hermitian symmetric space e 7 e 6 u 1 from projective superspace
Journal of High Energy Physics, 2013Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\mathcal{N}=2$ supersymmetric sigma model on the Cotangent Bundle over the Hermitian symmetric space E 7 /(E 6 × U(1)) in the projective superspace formalism, which is a manifest $\mathcal{N}=2$ off-shell superfield formulation in four-dimensional spacetime. To obtain this model we elaborate on the results developed in arXiv:0811.0218 and present a new closed formula for the Cotangent Bundle action, which is valid for all Hermitian symmetric spaces. We show that the structure of the Cotangent Bundle action is closely related to the analytic structure of the Kahler potential with respect to a uniform rescaling of coordinates.
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Cotangent Bundle over hermitian symmetric space e_7 e_6 times u 1 from projective superspace
arXiv: High Energy Physics - Theory, 2012Co-Authors: Masato Arai, Filip BlaschkeAbstract:We construct an $\cN=2$ supersymmetric sigma model on the Cotangent Bundle over the Hermitian symmetric space $E_7/(E_6\times U(1))$ in the projective superspace formalism, which is a manifest $\cN=2$ off-shell superfield formulation in four-dimensional spacetime. To obtain this model we elaborate on results developed in arXiv:0811.0218 and present a new closed formula for the Cotangent Bundle action, which is valid for all Hermitian symmetric spaces. We show that the structure of Cotangent Bundle action is intimately related to the analytic structure of the K\"ahler potential with respect to a uniform rescaling of coordinates.
