메뉴 건너뛰기




Volumn 9, Issue 3, 2009, Pages 1503-1583

Cohomology theories for homotopy algebras and noncommutative geometry

Author keywords

Cyclic cohomology; Harrison cohomology; Hodge decomposition; Infinityalgebra; Symplectic structure

Indexed keywords


EID: 72949094457     PISSN: 14722747     EISSN: 14722739     Source Type: Journal    
DOI: 10.2140/agt.2009.9.1503     Document Type: Article
Times cited : (28)

References (47)
  • 2
    • 0000918904 scopus 로고
    • Harrison homology, Hochschild homology and triples
    • MR0220799
    • M Barr, Harrison homology, Hochschild homology and triples, J. Algebra 8 (1968) 314-323 MR0220799
    • (1968) J. Algebra , vol.8 , pp. 314-323
    • Barr, M.1
  • 3
    • 48149104386 scopus 로고    scopus 로고
    • Transferring homotopy commutative algebraic structures
    • MR2440265
    • X Z Cheng, E Getzler, Transferring homotopy commutative algebraic structures, J. Pure Appl. Algebra 212 (2008) 2535-2542 MR2440265
    • (2008) J. Pure Appl. Algebra , vol.212 , pp. 2535-2542
    • Cheng, X.Z.1    Getzler, E.2
  • 4
    • 4243056625 scopus 로고    scopus 로고
    • On a theorem of Kontsevich
    • MR2026331
    • J Conant, K Vogtmann, On a theorem of Kontsevich, Algebr. Geom. Topol. 3 (2003) 1167-1224 MR2026331
    • (2003) Algebr. Geom. Topol. , vol.3 , pp. 1167-1224
    • Conant, J.1    Vogtmann, K.2
  • 6
    • 0036758167 scopus 로고    scopus 로고
    • Deformation theory of infinity algebras
    • MR1935035
    • A Fialowski, M Penkava, Deformation theory of infinity algebras, J. Algebra 255 (2002) 59-88 MR1935035
    • (2002) J. Algebra , vol.255 , pp. 59-88
    • Fialowski, A.1    Penkava, M.2
  • 7
    • 0001523110 scopus 로고
    • The cohomology structure of an associative ring
    • MR0161898
    • M Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math. (2) 78 (1963) 267-288 MR0161898
    • (1963) Ann. of Math. , vol.78 , Issue.2 , pp. 267-288
    • Gerstenhaber, M.1
  • 8
    • 1842698673 scopus 로고
    • A Hodgetype decomposition for commutative algebra cohomology
    • MR917209
    • M Gerstenhaber, S D Schack, A Hodgetype decomposition for commutative algebra cohomology, J. Pure Appl. Algebra 48 (1987) 229-247 MR917209
    • (1987) J. Pure Appl. Algebra , vol.48 , pp. 229-247
    • Gerstenhaber, M.1    Schack, S.D.2
  • 10
    • 0037085530 scopus 로고    scopus 로고
    • A Darboux theorem for Hamiltonian operators in the formal calculus of variations
    • MR1885831
    • E Getzler, A Darboux theorem for Hamiltonian operators in the formal calculus of variations, Duke Math. J. 111 (2002) 535-560 MR1885831
    • (2002) Duke Math. J. , vol.111 , pp. 535-560
    • Getzler, E.1
  • 12
    • 84972576237 scopus 로고
    • A∞-algebras and the cyclic bar complex
    • MR1046565
    • E Getzler, J D S Jones, A∞-algebras and the cyclic bar complex, Illinois J. Math. 34 (1990) 256-283 MR1046565
    • (1990) Illinois J. Math. , vol.34 , pp. 256-283
    • Getzler, E.1    Jones, J.D.S.2
  • 13
    • 0001384030 scopus 로고
    • Cyclic operads and cyclic homology
    • from, (editor S T Yau), Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, MR1358617
    • E Getzler, M M Kapranov, Cyclic operads and cyclic homology, from: Geometry, topology, & physics (editor S T Yau), Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press (1995) 167-201 MR1358617
    • (1995) Geometry, Topology, & Physics , pp. 167-201
    • Getzler, E.1    Kapranov, M.M.2
  • 14
    • 0035535890 scopus 로고    scopus 로고
    • Noncommutative symplectic geometry, quiver varieties, and operads
    • MR1839485
    • V Ginzburg, Noncommutative symplectic geometry, quiver varieties, and operads, Math. Res. Lett. 8 (2001) 377-400 MR1839485
    • (2001) Math. Res. Lett. , vol.8 , pp. 377-400
    • Ginzburg, V.1
  • 15
    • 51249177029 scopus 로고
    • The deformation theory of representations of fundamental groups of compact Kähler manifolds
    • MR972343
    • W M Goldman, J J Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Inst. Hautes Études Sci. Publ. Math. (1988) 43-96 MR972343
    • (1988) Inst. Hautes Études Sci. Publ. Math. , pp. 43-96
    • Goldman, W.M.1    Millson, J.J.2
  • 16
    • 18644385348 scopus 로고    scopus 로고
    • On the classification of Moore algebras and their deformations
    • MR2061569
    • A Hamilton, On the classification of Moore algebras and their deformations, Homology Homotopy Appl. 6 (2004) 87-107 MR2061569
    • (2004) Homology Homotopy Appl. , vol.6 , pp. 87-107
    • Hamilton, A.1
  • 17
    • 33645698537 scopus 로고    scopus 로고
    • Superanalogue of Kontsevich's theorem on graph homology
    • MR2223762
    • A Hamilton, A superanalogue of Kontsevich's theorem on graph homology, Lett. Math. Phys. 76 (2006) 37-55 MR2223762
    • (2006) Lett. Math. Phys. , vol.76 , pp. 37-55
    • Hamilton, A.1
  • 18
    • 63649097423 scopus 로고    scopus 로고
    • Characteristic classes of A∞-algebras
    • MR2395368
    • A Hamilton, A Lazarev, Characteristic classes of A∞-algebras, J. Homotopy Relat. Struct. 3 (2008) 65-111 MR2395368
    • (2008) J. Homotopy Relat. Struct. , vol.3 , pp. 65-111
    • Hamilton, A.1    Lazarev, A.2
  • 19
    • 84968466891 scopus 로고
    • Commutative algebras and cohomology
    • MR0142607
    • D K Harrison, Commutative algebras and cohomology, Trans. Amer. Math. Soc. 104 (1962) 191-204 MR0142607
    • (1962) Trans. Amer. Math. Soc. , vol.104 , pp. 191-204
    • Harrison, D.K.1
  • 20
    • 1842779829 scopus 로고    scopus 로고
    • Descent of Deligne groupoids
    • MR1439623
    • V Hinich, Descent of Deligne groupoids, Internat. Math. Res. Notices (1997) 223-239 MR1439623
    • (1997) Internat. Math. Res. Notices , pp. 223-239
    • Hinich, V.1
  • 21
    • 0009027411 scopus 로고
    • The algebraic structure in the homology of an A(∞)-algebra
    • MR720689
    • T V Kadeishvili, The algebraic structure in the homology of an A(∞)-algebra, Soobshch. Akad. Nauk Gruzin. SSR 108 (1982) MR720689
    • (1982) Soobshch. Akad. Nauk Gruzin. SSR. , pp. 108
    • Kadeishvili, T.V.1
  • 22
    • 0032217874 scopus 로고    scopus 로고
    • Noncommutative geometry based on commutator expansions
    • MR1662244
    • M Kapranov, Noncommutative geometry based on commutator expansions, J. Reine Angew. Math. 505 (1998) 73-118 MR1662244
    • (1998) J. Reine Angew. Math. , vol.505 , pp. 73-118
    • Kapranov, M.1
  • 23
    • 0003356644 scopus 로고
    • Quantum groups
    • Springer, MR1321145
    • C Kassel, Quantum groups, Graduate Texts in Math. 155, Springer (1995) MR1321145
    • (1995) Graduate Texts In Math. , vol.155
    • Kassel, C.1
  • 24
    • 0007370748 scopus 로고    scopus 로고
    • Introduction to A-infinity algebras and modules
    • MR1854636
    • B Keller, Introduction to A-infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1-35 MR1854636
    • (2001) Homology Homotopy Appl. , vol.3 , pp. 1-35
    • Keller, B.1
  • 25
    • 0000695814 scopus 로고
    • Formal (non)commutative symplectic geometry
    • from, (editors L Corwin, I Gel ″fand, J Lepowsky), Birkh äuser
    • M Kontsevich, Formal (non)commutative symplectic geometry, from: The Gel″ fand Mathematical Seminars, 1990-1992 (editors L Corwin, I Gel ″fand, J Lepowsky), Birkh äuser (1993) 173-187 MR1247289
    • (1993) The Gel′ Fand Mathematical Seminars, 1990-1992 , pp. 173-187
    • Kontsevich, M.1
  • 26
    • 0001499677 scopus 로고
    • Feynman diagrams and lowdimensional topology
    • from, First European Congress of Mathematics, Vol. II (Paris, 1992), Birkhäuser, MR1341841
    • M Kontsevich, Feynman diagrams and lowdimensional topology, from: First European Congress of Mathematics, Vol. II (Paris, 1992), Progr. Math. 120, Birkhäuser (1994) 97-121 MR1341841
    • (1994) Progr. Math. , vol.120 , pp. 97-121
    • Kontsevich, M.1
  • 27
    • 3843152796 scopus 로고    scopus 로고
    • Deformation quantization of Poisson manifolds
    • MR2062626
    • M Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003) 157-216 MR2062626
    • (2003) Lett. Math. Phys. , vol.66 , pp. 157-216
    • Kontsevich, M.1
  • 28
    • 0007156109 scopus 로고    scopus 로고
    • Noncommutative smooth spaces
    • from, (editors I M Gelfand, V S Retakh), Birkhäuser, MR1731635
    • M Kontsevich, A L Rosenberg, Noncommutative smooth spaces, from: The Gelfand Mathematical Seminars, 1996-1999 (editors I M Gelfand, V S Retakh), Birkhäuser (2000) 85-108 MR1731635
    • (2000) The Gelfand Mathematical Seminars, 1996-1999 , pp. 85-108
    • Kontsevich, M.1    Rosenberg, A.L.2
  • 31
    • 18644381086 scopus 로고    scopus 로고
    • Hochschild cohomology and moduli spaces of strongly homotopy associative algebras
    • MR1989615
    • A Lazarev, Hochschild cohomology and moduli spaces of strongly homotopy associative algebras, Homology Homotopy Appl. 5 (2003) 73-100 MR1989615
    • (2003) Homology Homotopy Appl. , vol.5 , pp. 73-100
    • Lazarev, A.1
  • 32
    • 0003246987 scopus 로고    scopus 로고
    • Cyclic homology
    • Wissenschaften, Springer, MR1600246, Appendix E by M O Ronco, Chapter 13 by the author in collaboration with T Pirashvili
    • J L Loday, Cyclic homology, Grund. der Math. Wissenschaften 301, Springer (1998) MR1600246 Appendix E by M O Ronco, Chapter 13 by the author in collaboration with T Pirashvili
    • (1998) Grund. Der Math. , vol.301
    • Loday, J.L.1
  • 33
    • 38249008826 scopus 로고
    • A cohomology theory for A(m)-algebras and applications
    • MR1191090
    • M Markl, A cohomology theory for A(m)-algebras and applications, J. Pure Appl. Algebra 83 (1992) 141-175 MR1191090
    • (1992) J. Pure Appl. Algebra , vol.83 , pp. 141-175
    • Markl, M.1
  • 34
    • 1042302998 scopus 로고    scopus 로고
    • Homotopy algebras are homotopy algebras
    • MR2034546
    • M Markl, Homotopy algebras are homotopy algebras, Forum Math. 16 (2004) 129-160 MR2034546
    • (2004) Forum Math. , vol.16 , pp. 129-160
    • Markl, M.1
  • 35
    • 0012947756 scopus 로고    scopus 로고
    • Operads in algebra, topology and physics
    • Amer. Math. Soc, MR1898414
    • M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monogr. 96, Amer. Math. Soc. (2002) MR1898414
    • (2002) Math. Surveys and Monogr. , vol.96
    • Markl, M.1    Shnider, S.2    Stasheff, J.3
  • 37
    • 38249024421 scopus 로고
    • A decomposition for the cyclic cohomology of a commutative algebra
    • MR1027747
    • T Natsume, S D Schack, A decomposition for the cyclic cohomology of a commutative algebra, J. Pure Appl. Algebra 61 (1989) 273-282 MR1027747
    • (1989) J. Pure Appl. Algebra , vol.61 , pp. 273-282
    • Natsume, T.1    Schack, S.D.2
  • 38
    • 0001948516 scopus 로고
    • A∞ algebras and the cohomology of moduli spaces
    • from: Lie groups and Lie algebras: E B Dynkin's Seminar (editors S G Gindikin, from: Lie groups and Lie algebras: E B Dynkin's Seminar (editors S G Gindikin, E B Vinberg), Amer. Math. Soc., MR1364455
    • M Penkava, A Schwarz, A∞ algebras and the cohomology of moduli spaces, from: Lie groups and Lie algebras: E B Dynkin's Seminar (editors S G Gindikin, from: Lie groups and Lie algebras: E B Dynkin's Seminar (editors S G Gindikin, E B Vinberg), Amer. Math. Soc. Transl. Ser. 2 169, Amer. Math. Soc. (1995) 91-107 MR1364455
    • (1995) Amer. Math. Soc. Transl. Ser. 2 , vol.169 , pp. 91-107
    • Penkava, M.1    Schwarz, A.2
  • 39
    • 2942751949 scopus 로고    scopus 로고
    • Extensions of homogeneous coordinate rings to A∞-algebras
    • MR2072342
    • A Polishchuk, Extensions of homogeneous coordinate rings to A∞-algebras, Homology Homotopy Appl. 5 (2003) 407-421 MR2072342
    • (2003) Homology Homotopy Appl. , vol.5 , pp. 407-421
    • Polishchuk, A.1
  • 40
    • 0001531057 scopus 로고
    • Rational homotopy theory
    • MR0258031
    • D Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969) 205-295 MR0258031
    • (1969) Ann. of Math. , vol.90 , Issue.2 , pp. 205-295
    • Quillen, D.1
  • 42
    • 84968509262 scopus 로고
    • Homotopy associativity of H -spaces. I
    • MR0158400
    • J Stasheff, Homotopy associativity of H -spaces. I, Trans. Amer. Math. Soc. 108 (1963) 275-292 MR0158400
    • (1963) Trans. Amer. Math. Soc. , vol.108 , pp. 275-292
    • Stasheff, J.1
  • 43
    • 84968509262 scopus 로고
    • Homotopy associativity of H -spaces. II
    • MR0158400
    • J Stasheff, Homotopy associativity of H -spaces. II, Trans. Amer. Math. Soc. 108 (1963) 293-312 MR0158400
    • (1963) Trans. Amer. Math. Soc , vol.108 , pp. 293-312
    • Stasheff, J.1
  • 44
    • 0000854675 scopus 로고
    • The intrinsic bracket on the deformation complex of an associative algebra
    • MR1239562
    • J Stasheff, The intrinsic bracket on the deformation complex of an associative algebra, J. Pure Appl. Algebra 89 (1993) 231-235 MR1239562
    • (1993) J. Pure Appl. Algebra , vol.89 , pp. 231-235
    • Stasheff, J.1
  • 46
    • 26444568665 scopus 로고    scopus 로고
    • Notes on universal algebra
    • from: Graphs and patterns in mathematics and theoretical physics (editors M Lyubich, L Takhtajan), Amer. Math. Soc., MR2131012
    • A A Voronov, Notes on universal algebra, from: Graphs and patterns in mathematics and theoretical physics (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 81-103 MR2131012
    • (2005) Proc. Sympos. Pure Math. , vol.73 , pp. 81-103
    • Voronov, A.A.1
  • 47
    • 13644277000 scopus 로고
    • Closed string field theory: Quantum action and the Batalin- Vilkovisky master equation
    • MR1203476
    • B Zwiebach, Closed string field theory: quantum action and the Batalin- Vilkovisky master equation, Nuclear Phys. B 390 (1993) 33-152 MR1203476
    • (1993) Nuclear Phys. B , vol.390 , pp. 33-152
    • Zwiebach, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.