메뉴 건너뛰기




Volumn 15, Issue 5, 1997, Pages 447-486

Tangent and Cotangent Lifts and Graded Lie Algebras Associated with Lie Algebroids

Author keywords

Cotangent lift; Fr licher Nijenhuis bracket; Lie algebroid; Poisson structure; Schouten bracket; Tangent lift

Indexed keywords


EID: 0001576518     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006519730920     Document Type: Article
Times cited : (53)

References (31)
  • 1
    • 51249166028 scopus 로고
    • Graded Poisson structures on the algebra of differential forms
    • Beltrán, J. V. and Monterde, J.: Graded Poisson structures on the algebra of differential forms, Comment. Math. Helv. 70 (1995), 383-402.
    • (1995) Comment. Math. Helv. , vol.70 , pp. 383-402
    • Beltrán, J.V.1    Monterde, J.2
  • 3
    • 0002722894 scopus 로고
    • Publications du Département de Mathématiques de l'Université Claude-Bernard de Lyon
    • Coste, A., Dazord, P. and Weinstein, A.: GroupoÉdes symplectiques, Publications du Département de Mathématiques de l'Université Claude-Bernard de Lyon, 1987, pp. 1-65.
    • (1987) GroupoÉdes Symplectiques , pp. 1-65
    • Coste, A.1    Dazord, P.2    Weinstein, A.3
  • 5
    • 0001691305 scopus 로고
    • Tangent Dirac structures
    • Courant, T. J.: Tangent Dirac structures, J. Phys. A 23 (1990), 5153-5160.
    • (1990) J. Phys. A , vol.23 , pp. 5153-5160
    • Courant, T.J.1
  • 6
    • 0003089719 scopus 로고
    • Extensions of the Poisson bracket to differential forms and multi-vector fields
    • Cabras, A. and Vinogradov, A. M.: Extensions of the Poisson bracket to differential forms and multi-vector fields, J. Geom. Phys. 9 (1992), 75-100.
    • (1992) J. Geom. Phys. , vol.9 , pp. 75-100
    • Cabras, A.1    Vinogradov, A.M.2
  • 7
    • 0002803925 scopus 로고
    • A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetric multivector fields
    • Dubois-Violette, M. and Michor, P.: A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetric multivector fields, Indag. Math. N. S. 6 (1995), 51-66.
    • (1995) Indag. Math. N. S. , vol.6 , pp. 51-66
    • Dubois-Violette, M.1    Michor, P.2
  • 8
    • 0000793354 scopus 로고
    • Theory of vector-valued differential forms, Part 1
    • Frölicher, A. and Nijenhuis, A.: Theory of vector-valued differential forms, Part 1, Indag. Math. 18 (1956), 338-359.
    • (1956) Indag. Math. , vol.18 , pp. 338-359
    • Frölicher, A.1    Nijenhuis, A.2
  • 9
    • 0031285815 scopus 로고    scopus 로고
    • Z-graded extensions of Poisson brackets
    • Grabowski, J.: Z-graded extensions of Poisson brackets, Rev. Math. Phys. 9 (1997), 1-27.
    • (1997) Rev. Math. Phys. , vol.9 , pp. 1-27
    • Grabowski, J.1
  • 10
    • 0002026758 scopus 로고
    • Tangent lifts of Poisson and related structures
    • Grabowski, J. and Urbański, P.: Tangent lifts of Poisson and related structures, J. Phys. A 28 (1995), 6743-6777.
    • (1995) J. Phys. A , vol.28 , pp. 6743-6777
    • Grabowski, J.1    Urbański, P.2
  • 11
    • 84942964667 scopus 로고
    • Poisson cohomology and quantization
    • Huebschmann, J.: Poisson cohomology and quantization, J. Reine Angew. Math. 408 (1990), 57-113.
    • (1990) J. Reine Angew. Math. , vol.408 , pp. 57-113
    • Huebschmann, J.1
  • 12
    • 0005215531 scopus 로고
    • Analogues of the objects of Lie group theory for nonlinear Poisson brackets
    • Karasev, M. V.: Analogues of the objects of Lie group theory for nonlinear Poisson brackets, Mat. USSR - Izv. 28 (1987), 497-527.
    • (1987) Mat. USSR - Izv. , vol.28 , pp. 497-527
    • Karasev, M.V.1
  • 14
    • 0001133433 scopus 로고
    • Exact Gerstenhaber algebras and Lie bialgebroids
    • Kosmann-Schwarzbach, Y.: Exact Gerstenhaber algebras and Lie bialgebroids, Acta Applicandae Math. 41 (1995), 153-165.
    • (1995) Acta Applicandae Math. , vol.41 , pp. 153-165
    • Kosmann-Schwarzbach, Y.1
  • 17
  • 18
    • 0002055139 scopus 로고
    • Schouten bracket and canonical algebra, II
    • Borysovich, Yu. G. and Gliklikh, Yu. E. (eds.), Lect. Notes Math.
    • Krasil'shchik, I.: Schouten bracket and canonical algebra, II, in Borysovich, Yu. G. and Gliklikh, Yu. E. (eds.), Studies and Appl. III, Global Analysis, Lect. Notes Math., Vol. 1334, 1988, pp. 79-100.
    • (1988) Studies and Appl. III, Global Analysis , vol.1334 , pp. 79-100
    • Krasil'shchik, I.1
  • 19
    • 0242336451 scopus 로고
    • Supercanonical algebras and Schouten brackets
    • Krasil'shchik, I.: Supercanonical algebras and Schouten brackets, Mathematical Notes 49 (1991), 70-76.
    • (1991) Mathematical Notes , vol.49 , pp. 70-76
    • Krasil'shchik, I.1
  • 21
    • 0000636313 scopus 로고
    • Double Lie algebroids and second-order geometry I
    • Mackenzie, K. C. H.: Double Lie algebroids and second-order geometry I, Adv. Math. 94 (1992), 180-239.
    • (1992) Adv. Math. , vol.94 , pp. 180-239
    • Mackenzie, K.C.H.1
  • 22
    • 84973999707 scopus 로고
    • Lie bialgebroids and Poisson groupoids
    • Mackenzie, K. C. H. and Xu, P.: Lie bialgebroids and Poisson groupoids, Duke Math. J. 73 (1994), 415-452.
    • (1994) Duke Math. J. , vol.73 , pp. 415-452
    • Mackenzie, K.C.H.1    Xu, P.2
  • 23
    • 0002566063 scopus 로고
    • A generalization of Hamiltonian mechanics
    • Michor, P.: A generalization of Hamiltonian mechanics, J. Geom. Phys. 2 (1985), 67-82.
    • (1985) J. Geom. Phys. , vol.2 , pp. 67-82
    • Michor, P.1
  • 25
    • 0001031484 scopus 로고
    • Jacobi-type identities for bilinear differential concomitants of certain tensor fields I
    • Nijenhuis, A.: Jacobi-type identities for bilinear differential concomitants of certain tensor fields I, Indag. Math. 17 (1955), 390-403.
    • (1955) Indag. Math. , vol.17 , pp. 390-403
    • Nijenhuis, A.1
  • 26
    • 0002709811 scopus 로고
    • Deformations of Lie algebra structures
    • Nijenhuis, A. and Richardson, R.: Deformations of Lie algebra structures, J. Math. Mech. 171 (1967), 89-106.
    • (1967) J. Math. Mech. , vol.171 , pp. 89-106
    • Nijenhuis, A.1    Richardson, R.2
  • 28
    • 0000865548 scopus 로고
    • Über Differentialkonkomitanten zweier kontravarianter Größen
    • Schouten, J. A.: Über Differentialkonkomitanten zweier kontravarianter Größen, Indag. Math. 2 (1940), 449-452.
    • (1940) Indag. Math. , vol.2 , pp. 449-452
    • Schouten, J.A.1
  • 29
    • 21144460384 scopus 로고
    • An algebraic approach to the Lie algebra of Cartan type
    • Skryabin, S. M.: An algebraic approach to the Lie algebra of Cartan type, Comm. Algebra 21 (1993), 1229-1336.
    • (1993) Comm. Algebra , vol.21 , pp. 1229-1336
    • Skryabin, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.