机构:
Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 65892, Riyadh 11566, Saudi ArabiaImam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 65892, Riyadh 11566, Saudi Arabia
Al-Dayel, Ibrahim
[1
]
Aloui, Foued
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Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 65892, Riyadh 11566, Saudi ArabiaImam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 65892, Riyadh 11566, Saudi Arabia
Aloui, Foued
[1
]
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Deshmukh, Sharief
[2
]
机构:
[1] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, POB 65892, Riyadh 11566, Saudi Arabia
[2] King Saud Univ, Dept Math, Riyadh 11495, Saudi Arabia
Let G be a Poisson-Lie group equipped with a left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on G to the tangent bundle TG of G. In this paper, we induce a left invariant contravariant pseudo-Riemannian metric on the tangent bundle TG, and we express in different cases the contravariant Levi-Civita connection and curvature of TG in terms of the contravariant Levi-Civita connection and the curvature of G. We prove that the space of differential forms omega*(G) on G is a differential graded Poisson algebra if, and only if, omega*(TG) is a differential graded Poisson algebra. Moreover, we show that G is a pseudo-Riemannian Poisson-Lie group if, and only if, the Sanchez de Alvarez tangent Poisson-Lie group TG is also a pseudo-Riemannian Poisson-Lie group. Finally, some examples of pseudo-Riemannian tangent Poisson-Lie groups are given.
机构:
Penn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USAPenn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USA
Bojowald, M
Strobl, T
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机构:Penn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USA
机构:
Univ Santiago de Compostela, Fac Math, Santiago De Compostela 15782, SpainUniv Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain
Ferreiro-Subrido, M.
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Garcia-Rio, E.
Vazquez-Lorenzo, R.
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IES Ribadeo Dionisio Gamallo, Ribadeo 27700, SpainUniv Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain
机构:
Vietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam
Can Tho Univ, Coll Nat Sci, Can Tho City, VietnamVietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam
Nguyen, Tu T. C.
Le, Vu A.
论文数: 0引用数: 0
h-index: 0
机构:
Vietnam Natl Univ, Univ Econ & Law, Fac Econ Math, Ho Chi Minh City, VietnamVietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam
机构:
Penn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USAPenn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USA
Bojowald, M
Strobl, T
论文数: 0引用数: 0
h-index: 0
机构:Penn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USA
机构:
Univ Santiago de Compostela, Fac Math, Santiago De Compostela 15782, SpainUniv Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain
Ferreiro-Subrido, M.
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机构:
Garcia-Rio, E.
Vazquez-Lorenzo, R.
论文数: 0引用数: 0
h-index: 0
机构:
IES Ribadeo Dionisio Gamallo, Ribadeo 27700, SpainUniv Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain
机构:
Vietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam
Can Tho Univ, Coll Nat Sci, Can Tho City, VietnamVietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam
Nguyen, Tu T. C.
Le, Vu A.
论文数: 0引用数: 0
h-index: 0
机构:
Vietnam Natl Univ, Univ Econ & Law, Fac Econ Math, Ho Chi Minh City, VietnamVietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam