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Picard group of isotropic realizations of twisted Poisson manifolds
Infinitesimally natural principal bundles
1. | Universiteit Utrecht, Budapestlaan 6, 3584 CD Utrecht, Netherlands |
References:
[1] |
A. Banyaga, The Structure of Classical Diffeomorphism Groups, volume 400 of Mathematics and its Applications,, Kluwer Academic Publishers Group, (1997).
doi: 10.1007/978-1-4757-6800-8. |
[2] |
D. W. Barnes, Nilpotency of Lie algebras,, Math. Zeitschr., 79 (1962), 237.
doi: 10.1007/BF01193118. |
[3] |
M. Berg, C. DeWitt-Morette, S. Gwo and E. Kramer, The pin groups in physics: C, P and T,, Rev. Math. Phys., 13 (2001), 953.
doi: 10.1142/S0129055X01000922. |
[4] |
M. Crainic and R. L. Fernandes, Integrability of Lie brackets,, Ann. of Math., 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[5] |
D. B. A. Epstein and W. P. Thurston, Transformation groups and natural bundles,, Proc. London Math. Soc., 38 (1979), 219.
doi: 10.1112/plms/s3-38.2.219. |
[6] |
D. B. Fuks, Cohomology of Infinite Dimensional Lie Algebras,, Contemporary Soviet Mathematics, (1986).
|
[7] |
H. Glöckner, Differentiable mappings between spaces of sections, 2002., arXiv:1308.1172., (). Google Scholar |
[8] |
J. Grabowski, A. Kotov and N. Poncin, Geometric structures encoded in the Lie structure of an Atiyah algebroid,, Transform. Groups, 16 (2011), 137.
doi: 10.1007/s00031-011-9126-9. |
[9] |
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory,, Graduate Texts in Mathematics, (1972).
|
[10] |
A. W. Knapp, Lie Groups Beyond an Introduction,, Birkhäuser, (1996).
doi: 10.1007/978-1-4757-2453-0. |
[11] |
H. B. Lawson and M.-L. Michelsohn, Spin geometry,, Princeton University Press, (1994). Google Scholar |
[12] |
P. B. A. Lecomte, Sur la suite exacte canonique associée à un fibré principal,, Bulletin de la S. M. F., 113 (1985), 259.
|
[13] |
K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, volume 124 of London Mathematical Society Lecture Note Series., Cambridge University Press, (1987).
doi: 10.1017/CBO9780511661839. |
[14] |
I. Moerdijk and J. Mrčun, On integrability of infinitesimal actions,, Amer. J. Math., 124 (2002), 567.
doi: 10.1353/ajm.2002.0019. |
[15] |
S. Morrison, Classifying Spinor Structures,, Master's thesis, (2001). Google Scholar |
[16] |
K. C. H. Mackenzie and P. Xu, Integration of Lie bialgebroids,, Topology, 39 (2000), 445.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
A. Nijenhuis, Theory of the Geometric Object, 1952., Doctoral thesis, ().
|
[18] |
A. Nijenhuis, Geometric aspects of formal differential operations on tensors fields,, In Proc. Internat. Congress Math. 1958, (1958), 463.
|
[19] |
A. Nijenhuis, Natural bundles and their general properties. Geometric objects revisited,, In Differential geometry (in honor of Kentaro Yano), (1972), 317.
|
[20] |
R. S. Palais and C. L. Terng, Natural bundles have finite order,, Topology, 19 (1977), 271.
|
[21] |
J. Peetre, Réctification (sic) à l'article «une caractérisation abstraite des opérateurs différentiels»,, Math. Scand., 8 (1960), 116.
|
[22] |
J. Pradines, Théorie de Lie pour les groupoides différentiables, relation entre propriétés locales et globales,, Comptes Rendus Acad. Sci. Paris A, 263 (1966), 907.
|
[23] |
S. E. Salvioli, On the theory of geometric objects,, J. Diff. Geom., 7 (1972), 257.
|
[24] |
J. A. Schouten and J. Haantjes, On the Theory of the Geometric Object,, Proc. London Math. Soc., S2-42 (1937), 2.
doi: 10.1112/plms/s2-42.1.356. |
[25] |
M. E. Shanks and L. E. Pursell, The Lie algebra of a smooth manifold,, Proc. Amer. Math. Soc., 5 (1954), 468.
doi: 10.1090/S0002-9939-1954-0064764-3. |
[26] |
Kōji Shiga and Toru Tsujishita, Differential representations of vector fields,, Kōdai Math. Sem. Rep., 28 (): 214.
|
[27] |
F. Takens, Derivations of vector fields,, Comp. Math., 26 (1973), 151.
|
[28] |
C. L. Terng, Natural vector bundles and natural differential operators,, Am. J. Math., 100 (1978), 775.
doi: 10.2307/2373910. |
[29] |
A. Wundheiler, Objekte, Invarianten und Klassifikation der Geometrie,, Abh. Sem. Vektor Tenzoranal. Moskau, 4 (1937), 366. Google Scholar |
show all references
References:
[1] |
A. Banyaga, The Structure of Classical Diffeomorphism Groups, volume 400 of Mathematics and its Applications,, Kluwer Academic Publishers Group, (1997).
doi: 10.1007/978-1-4757-6800-8. |
[2] |
D. W. Barnes, Nilpotency of Lie algebras,, Math. Zeitschr., 79 (1962), 237.
doi: 10.1007/BF01193118. |
[3] |
M. Berg, C. DeWitt-Morette, S. Gwo and E. Kramer, The pin groups in physics: C, P and T,, Rev. Math. Phys., 13 (2001), 953.
doi: 10.1142/S0129055X01000922. |
[4] |
M. Crainic and R. L. Fernandes, Integrability of Lie brackets,, Ann. of Math., 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[5] |
D. B. A. Epstein and W. P. Thurston, Transformation groups and natural bundles,, Proc. London Math. Soc., 38 (1979), 219.
doi: 10.1112/plms/s3-38.2.219. |
[6] |
D. B. Fuks, Cohomology of Infinite Dimensional Lie Algebras,, Contemporary Soviet Mathematics, (1986).
|
[7] |
H. Glöckner, Differentiable mappings between spaces of sections, 2002., arXiv:1308.1172., (). Google Scholar |
[8] |
J. Grabowski, A. Kotov and N. Poncin, Geometric structures encoded in the Lie structure of an Atiyah algebroid,, Transform. Groups, 16 (2011), 137.
doi: 10.1007/s00031-011-9126-9. |
[9] |
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory,, Graduate Texts in Mathematics, (1972).
|
[10] |
A. W. Knapp, Lie Groups Beyond an Introduction,, Birkhäuser, (1996).
doi: 10.1007/978-1-4757-2453-0. |
[11] |
H. B. Lawson and M.-L. Michelsohn, Spin geometry,, Princeton University Press, (1994). Google Scholar |
[12] |
P. B. A. Lecomte, Sur la suite exacte canonique associée à un fibré principal,, Bulletin de la S. M. F., 113 (1985), 259.
|
[13] |
K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, volume 124 of London Mathematical Society Lecture Note Series., Cambridge University Press, (1987).
doi: 10.1017/CBO9780511661839. |
[14] |
I. Moerdijk and J. Mrčun, On integrability of infinitesimal actions,, Amer. J. Math., 124 (2002), 567.
doi: 10.1353/ajm.2002.0019. |
[15] |
S. Morrison, Classifying Spinor Structures,, Master's thesis, (2001). Google Scholar |
[16] |
K. C. H. Mackenzie and P. Xu, Integration of Lie bialgebroids,, Topology, 39 (2000), 445.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
A. Nijenhuis, Theory of the Geometric Object, 1952., Doctoral thesis, ().
|
[18] |
A. Nijenhuis, Geometric aspects of formal differential operations on tensors fields,, In Proc. Internat. Congress Math. 1958, (1958), 463.
|
[19] |
A. Nijenhuis, Natural bundles and their general properties. Geometric objects revisited,, In Differential geometry (in honor of Kentaro Yano), (1972), 317.
|
[20] |
R. S. Palais and C. L. Terng, Natural bundles have finite order,, Topology, 19 (1977), 271.
|
[21] |
J. Peetre, Réctification (sic) à l'article «une caractérisation abstraite des opérateurs différentiels»,, Math. Scand., 8 (1960), 116.
|
[22] |
J. Pradines, Théorie de Lie pour les groupoides différentiables, relation entre propriétés locales et globales,, Comptes Rendus Acad. Sci. Paris A, 263 (1966), 907.
|
[23] |
S. E. Salvioli, On the theory of geometric objects,, J. Diff. Geom., 7 (1972), 257.
|
[24] |
J. A. Schouten and J. Haantjes, On the Theory of the Geometric Object,, Proc. London Math. Soc., S2-42 (1937), 2.
doi: 10.1112/plms/s2-42.1.356. |
[25] |
M. E. Shanks and L. E. Pursell, The Lie algebra of a smooth manifold,, Proc. Amer. Math. Soc., 5 (1954), 468.
doi: 10.1090/S0002-9939-1954-0064764-3. |
[26] |
Kōji Shiga and Toru Tsujishita, Differential representations of vector fields,, Kōdai Math. Sem. Rep., 28 (): 214.
|
[27] |
F. Takens, Derivations of vector fields,, Comp. Math., 26 (1973), 151.
|
[28] |
C. L. Terng, Natural vector bundles and natural differential operators,, Am. J. Math., 100 (1978), 775.
doi: 10.2307/2373910. |
[29] |
A. Wundheiler, Objekte, Invarianten und Klassifikation der Geometrie,, Abh. Sem. Vektor Tenzoranal. Moskau, 4 (1937), 366. Google Scholar |
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