메뉴 건너뛰기




Volumn 46, Issue 5, 1996, Pages 1243-1274

From poisson algebras to Gerstenhaber algebras

Author keywords

Cohomology of associative and Lie algebras; Generalized BV algebras; Gerstenhaber algebras; Graded Lie algebras; Koszul bracket; Loday (Leibniz) algebras; Poisson algebras; Poisson calculus; Vinogradov bracket

Indexed keywords


EID: 0030376495     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1547     Document Type: Article
Times cited : (175)

References (43)
  • 1
    • 85033134488 scopus 로고    scopus 로고
    • On some generalizations of Batalin-Vilkovisky algebras
    • to appear
    • F. AKMAN, On some generalizations of Batalin-Vilkovisky algebras, J. Pure Appl. Alg., to appear.
    • J. Pure Appl. Alg.
    • Akman, F.1
  • 2
    • 51249166028 scopus 로고
    • Graded Poisson structures on the algebra of differential forms
    • J.V. BELTRÁN AND J. MONTERDE, Graded Poisson structures on the algebra of differential forms, Comment. Math. Helvetici, 70 (1995), 383-402.
    • (1995) Comment. Math. Helvetici , vol.70 , pp. 383-402
    • Beltrán, J.V.1    Monterde, J.2
  • 4
    • 85033760136 scopus 로고
    • 3 cohomology
    • G. Aktas, C. Sadioglu, M. Serdaroglu, eds
    • 3 cohomology, Lect. Notes Phys. 447, G. Aktas, C. Sadioglu, M. Serdaroglu, eds. (1995), pp. 283-291.
    • (1995) Lect. Notes Phys. , vol.447 , pp. 283-291
    • Bouwknegt, P.1    Pilch, K.2
  • 5
    • 0002280063 scopus 로고
    • Théorie des opérateurs différentiels gradués sur les formes différentielles
    • C. BUTTIN, Théorie des opérateurs différentiels gradués sur les formes différentielles, Bull. Soc. Math. Fr., 102 (1) (1974), 49-73.
    • (1974) Bull. Soc. Math. Fr. , vol.102 , Issue.1 , pp. 49-73
    • Buttin, C.1
  • 6
    • 0003089719 scopus 로고
    • Extensions of the Poisson bracket to differential forms and multi-vector fields
    • A. CABRAS and A.M. VINOGRADOV, 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
    • 35949042229 scopus 로고
    • Graded Lie algebras in mathematics and physics
    • L. CORWIN, Yu. NEEMAN and S. STERNBERG, Graded Lie algebras in mathematics and physics, Rev. Mod. Phys., 47 (1975), 573-603.
    • (1975) Rev. Mod. Phys. , vol.47 , pp. 573-603
    • Corwin, L.1    Neeman, Yu.2    Sternberg, S.3
  • 10
    • 0345835511 scopus 로고
    • Hamiltonian operators and Hochschild homologies
    • Yu.L. DALETSKY and B.L. TSYGAN, Hamiltonian operators and Hochschild homologies, Funct. Anal. Appl., 19 (4) (1985), 319-321.
    • (1985) Funct. Anal. Appl. , vol.19 , Issue.4 , pp. 319-321
    • Daletsky, Yu.L.1    Tsygan, B.L.2
  • 11
    • 0000734746 scopus 로고
    • Formal deformations of the Poisson-Lie algebra of a symplectic manifold and star-products
    • M. Gerstenhaber and M. Hazewinkel, eds., Kluwer
    • M. de WILDE and P. LECOMTE, Formal deformations of the Poisson-Lie algebra of a symplectic manifold and star-products, in Deformation Theory of Algebras and Structures and Applications, M. Gerstenhaber and M. Hazewinkel, eds., 897-960, Kluwer, 1988.
    • (1988) Deformation Theory of Algebras and Structures and Applications , pp. 897-960
    • De Wilde, M.1    Lecomte, P.2
  • 12
    • 0000481618 scopus 로고
    • Quantum Groups
    • Proc. Int. Congress Math. Berkeley
    • V.G. DRINFELD, Quantum Groups, Proc. Int. Congress Math. Berkeley, Amer. Math. Soc., (1987), 798-820.
    • (1987) Amer. Math. Soc. , pp. 798-820
    • Drinfeld, V.G.1
  • 13
    • 85033758893 scopus 로고    scopus 로고
    • The Frölicher-Nijenhuis bracket for derivation based non commutative differential forms
    • to appear
    • M. DUBOIS-VIOLETTE and P. MICHOR, The Frölicher-Nijenhuis bracket for derivation based non commutative differential forms, J. Pure Appl. Alg., to appear.
    • J. Pure Appl. Alg.
    • Dubois-Violette, M.1    Michor, P.2
  • 15
    • 0000793355 scopus 로고
    • Theory of vector-valued differential forms. Part I
    • A. FRÖLICHER and A. NIJENHUIS, Theory of vector-valued differential forms. Part I, Indag. Math., 18 (1956), 338-359.
    • (1956) Indag. Math. , vol.18 , pp. 338-359
    • Frölicher, A.1    Nijenhuis, A.2
  • 16
    • 0011625388 scopus 로고
    • On a variant of noncommutative differential geometry
    • I.M. GELFAND, Yu.L. DALETSKII and B.L. TSYGAN, On a variant of noncommutative differential geometry, Soviet Math. Dokl., 40 (2) (1989), 422-426.
    • (1989) Soviet Math. Dokl. , vol.40 , Issue.2 , pp. 422-426
    • Gelfand, I.M.1    Daletskii, Yu.L.2    Tsygan, B.L.3
  • 17
    • 0001523110 scopus 로고
    • The cohomology structure of an associative ring
    • M. GERSTENHABER, The cohomology structure of an associative ring, Ann. Math., 78 (1963), 267-288.
    • (1963) Ann. Math. , vol.78 , pp. 267-288
    • Gerstenhaber, M.1
  • 19
    • 0002568626 scopus 로고
    • Algebras, bialgebras, quantum groups, and algebraic deformations
    • M. GERSTENHABER and S.D. SCHACK, Algebras, bialgebras, quantum groups, and algebraic deformations, Contemporary Math., 134 (1992), 51-92.
    • (1992) Contemporary Math. , vol.134 , pp. 51-92
    • Gerstenhaber, M.1    Schack, S.D.2
  • 20
    • 21344494005 scopus 로고
    • Batalin-Vilkovisky algebras and two-dimensional topological field theories
    • E. GETZLER, Batalin-Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys., 159 (1994), 265-285.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 265-285
    • Getzler, E.1
  • 21
    • 33744535598 scopus 로고
    • On operad structures of moduli spaces and string theory
    • T. KIMURA, J. STASHEFF and A.A. VORONOV, On operad structures of moduli spaces and string theory, Comm. Math. Phys., 171 (1995), 1-25.
    • (1995) Comm. Math. Phys. , vol.171 , pp. 1-25
    • Kimura, T.1    Stasheff, J.2    Voronov, A.A.3
  • 22
    • 0000114031 scopus 로고
    • Jacobian quasi-bialgebi as and quasi-Poisson Lie groups
    • Y. KOSMANN-SCHWARZBACH, Jacobian quasi-bialgebi as and quasi-Poisson Lie groups, Contemporary Math., 132 (1992), 459-489.
    • (1992) Contemporary Math. , vol.132 , pp. 459-489
    • Kosmann-Schwarzbach, Y.1
  • 23
    • 0001133433 scopus 로고
    • Exact. Gerstenhaber algebras and Lie bialgebroids
    • Y. KOSMANN-SCHWARZBACH, 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
  • 25
    • 0000834553 scopus 로고
    • Graded manifolds, graded Lie theory and prequantization
    • B. KOSTANT, Graded manifolds, graded Lie theory and prequantization, Lect. Notes Math., 570 (1977), 177-30.
    • (1977) Lect. Notes Math. , vol.570 , pp. 177-230
    • Kostant, B.1
  • 26
    • 0003098983 scopus 로고
    • Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras
    • B. KOSTANT and S. STERNBERG, Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras, Ann. Phys., 176 (1987), 49-113.
    • (1987) Ann. Phys. , vol.176 , pp. 49-113
    • Kostant, B.1    Sternberg, S.2
  • 27
    • 0001052135 scopus 로고
    • Crochet de Schouten-Nijenhuis et cohomologie, in Elie Cartan et les mathématiques d'aujourd'hui
    • hors série
    • J.-L. KOSZUL, Crochet de Schouten-Nijenhuis et cohomologie, in Elie Cartan et les mathématiques d'aujourd'hui, Astérisque, hors série (1985), 257-271.
    • (1985) Astérisque , pp. 257-271
    • Koszul, J.-L.1
  • 28
    • 0347727297 scopus 로고
    • unpublished notes
    • J.-L. KOSZUL, unpublished notes (1990).
    • (1990)
    • Koszul, J.-L.1
  • 30
    • 0242336451 scopus 로고
    • Supercanonical algebras and Schouten brackets
    • I. KRASILSHCHIK, Supercanonical algebras and Schouten brackets, Mathematical Notes, 49 (1) (1991), 70-76.
    • (1991) Mathematical Notes , vol.49 , Issue.1 , pp. 70-76
    • Krasilshchik, I.1
  • 31
    • 0002899624 scopus 로고
    • The multigraded Nijenhuis-Richardson algebra, its universal property and applications
    • P. LECOMTE, P.W. MICHOR and H. SCHICKETANZ, The multigraded Nijenhuis-Richardson algebra, its universal property and applications, J. Pure Appl. Alg., 77 (1992), 87-102.
    • (1992) J. Pure Appl. Alg. , vol.77 , pp. 87-102
    • Lecomte, P.1    Michor, P.W.2    Schicketanz, H.3
  • 33
    • 0003358374 scopus 로고
    • Cyclic homology
    • Springer-Verlag
    • J.-L. LODAY, Cyclic homology, Grund. Math. Wiss. 301, Springer-Verlag, 1992.
    • (1992) Grund. Math. Wiss. , vol.301
    • Loday, J.-L.1
  • 34
    • 0002390971 scopus 로고
    • Une version non commutative des algèbres de Lie : Les algèbres de Leibniz
    • J.-L. LODAY, Une version non commutative des algèbres de Lie : les algèbres de Leibniz, L'Enseignement Mathématique, 39 (1993), 269-293.
    • (1993) L'Enseignement Mathématique , vol.39 , pp. 269-293
    • Loday, J.-L.1
  • 35
    • 0001328830 scopus 로고
    • New perspectives on the BRST-algebraic structure in string theory
    • B.H. LIAN and G. J. ZUCKERMAN, New perspectives on the BRST-algebraic structure in string theory, Comm. Math. Phys., 154 (1993), 613-646.
    • (1993) Comm. Math. Phys. , vol.154 , pp. 613-646
    • Lian, B.H.1    Zuckerman, G.J.2
  • 36
    • 0002566063 scopus 로고
    • A generalization of Hamiltonian mechanics
    • P.W. MICHOR, A generalization of Hamiltonian mechanics, J. Geom. Phys., 2 (2) (1985), 67-82.
    • (1985) J. Geom. Phys. , vol.2 , Issue.2 , pp. 67-82
    • Michor, P.W.1
  • 37
    • 0347727290 scopus 로고
    • The graded Lie algebras of an algebra
    • A. NIJENHUIS, The graded Lie algebras of an algebra. Indag. Math., 29 (1967), 475-486.
    • (1967) Indag. Math. , vol.29 , pp. 475-486
    • Nijenhuis, A.1
  • 38
    • 0002709811 scopus 로고
    • Deformations of Lie algebra structures
    • A. NIJENHUIS and R. RICHARDSON, 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
  • 39
    • 0000679063 scopus 로고
    • On some algebraic structures arising in string theory
    • R. Penner and S.T. Yau, eds., International Press
    • M. PENKAVA and A. SCHWARZ, On some algebraic structures arising in string theory, in Perspectives in Mathematical Physics, vol. 3, R. Penner and S.T. Yau, eds., International Press, 1994.
    • (1994) Perspectives in Mathematical Physics , vol.3
    • Penkava, M.1    Schwarz, A.2
  • 40
    • 0001442173 scopus 로고
    • Algèbres de Lie graduées et quantification
    • Symplectic Geometry and Mathematical Physics, P. Donato et al., eds., Birkhäuser
    • C. ROGER, Algèbres de Lie graduées et quantification, in Symplectic Geometry and Mathematical Physics, P. Donato et al., eds., Progress in Math. 99, Birkhäuser, (1991), pp. 374-421.
    • (1991) Progress in Math. , vol.99 , pp. 374-421
    • Roger, C.1
  • 41
    • 0003246009 scopus 로고
    • Lectures on the Geometry of Poisson Manifolds
    • Birkhäuser
    • I. VAISMAN, Lectures on the Geometry of Poisson Manifolds, Progress in Math. 118, Birkhäuser (1994).
    • (1994) Progress in Math. , vol.118
    • Vaisman, I.1
  • 42
    • 0010177882 scopus 로고
    • Unification of Schouten-Nijenhuis and Frölicher-Nijenhuis brackets, cohomology and super-differential operators
    • A.M. VINOGRADOV, Unification of Schouten-Nijenhuis and Frölicher-Nijenhuis brackets, cohomology and super-differential operators, Mat. Zametki, 47 (6), 138-140 (1990).
    • (1990) Mat. Zametki , vol.47 , Issue.6 , pp. 138-140
    • Vinogradov, A.M.1
  • 43
    • 0000513682 scopus 로고
    • A note on the antibracket formalism
    • E. WITTEN, A note on the antibracket formalism, Modern Phys. Lett. A, 5 (7) (1990), 487-494.
    • (1990) Modern Phys. Lett. A , vol.5 , Issue.7 , pp. 487-494
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.