-
Previous Article
A weak approach to the stochastic deformation of classical mechanics
- JGM Home
- This Issue
-
Next Article
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, Dordrecht, 1997.
doi: 10.1007/978-1-4757-6800-8. |
[2] |
D. W. Barnes, Nilpotency of Lie algebras, Math. Zeitschr., 79 (1962), 237-238.
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), 953-1034.
doi: 10.1142/S0129055X01000922. |
[4] |
M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Ann. of Math., 157 (2003), 575-620.
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), 219-236.
doi: 10.1112/plms/s3-38.2.219. |
[6] |
D. B. Fuks, Cohomology of Infinite Dimensional Lie Algebras, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986. |
[7] |
H. Glöckner, Differentiable mappings between spaces of sections, 2002. arXiv:1308.1172. |
[8] |
J. Grabowski, A. Kotov and N. Poncin, Geometric structures encoded in the Lie structure of an Atiyah algebroid, Transform. Groups, 16 (2011), 137-160.
doi: 10.1007/s00031-011-9126-9. |
[9] |
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1972. |
[10] |
A. W. Knapp, Lie Groups Beyond an Introduction, Birkhäuser, Boston, first edition, 1996.
doi: 10.1007/978-1-4757-2453-0. |
[11] |
H. B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton University Press, second edition, 1994. |
[12] |
P. B. A. Lecomte, Sur la suite exacte canonique associée à un fibré principal, Bulletin de la S. M. F., 113 (1985), 259-271. |
[13] |
K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, volume 124 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1987.
doi: 10.1017/CBO9780511661839. |
[14] |
I. Moerdijk and J. Mrčun, On integrability of infinitesimal actions, Amer. J. Math., 124 (2002), 567-593.
doi: 10.1353/ajm.2002.0019. |
[15] |
S. Morrison, Classifying Spinor Structures, Master's thesis, University of New South Wales, 2001. |
[16] |
K. C. H. Mackenzie and P. Xu, Integration of Lie bialgebroids, Topology, 39 (2000), 445-467.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
A. Nijenhuis, Theory of the Geometric Object, 1952. Doctoral thesis, Universiteit van Amsterdam. |
[18] |
A. Nijenhuis, Geometric aspects of formal differential operations on tensors fields, In Proc. Internat. Congress Math. 1958, pages 463-469. Cambridge Univ. Press, New York, 1960. |
[19] |
A. Nijenhuis, Natural bundles and their general properties. Geometric objects revisited, In Differential geometry (in honor of Kentaro Yano), pages 317-334. Kinokuniya, Tokyo, 1972. |
[20] |
R. S. Palais and C. L. Terng, Natural bundles have finite order, Topology, 19 (1977), 271-277. |
[21] |
J. Peetre, Réctification (sic) à l'article «une caractérisation abstraite des opérateurs différentiels», Math. Scand., 8 (1960), 116-120. |
[22] |
J. Pradines, Théorie de Lie pour les groupoides différentiables, relation entre propriétés locales et globales, Comptes Rendus Acad. Sci. Paris A, 263 (1966), 907-910. |
[23] |
S. E. Salvioli, On the theory of geometric objects, J. Diff. Geom., 7 (1972), 257-278. |
[24] |
J. A. Schouten and J. Haantjes, On the Theory of the Geometric Object, Proc. London Math. Soc., S2-42 (1937), 356-376.
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), 468-472.
doi: 10.1090/S0002-9939-1954-0064764-3. |
[26] |
Kōji Shiga and Toru Tsujishita, Differential representations of vector fields, Kōdai Math. Sem. Rep., 28 (1976/77), 214-225. |
[27] |
F. Takens, Derivations of vector fields, Comp. Math., 26 (1973), 151-158. |
[28] |
C. L. Terng, Natural vector bundles and natural differential operators, Am. J. Math., 100 (1978), 775-828.
doi: 10.2307/2373910. |
[29] |
A. Wundheiler, Objekte, Invarianten und Klassifikation der Geometrie, Abh. Sem. Vektor Tenzoranal. Moskau, 4 (1937), 366-375. |
show all references
References:
[1] |
A. Banyaga, The Structure of Classical Diffeomorphism Groups, volume 400 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 1997.
doi: 10.1007/978-1-4757-6800-8. |
[2] |
D. W. Barnes, Nilpotency of Lie algebras, Math. Zeitschr., 79 (1962), 237-238.
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), 953-1034.
doi: 10.1142/S0129055X01000922. |
[4] |
M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Ann. of Math., 157 (2003), 575-620.
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), 219-236.
doi: 10.1112/plms/s3-38.2.219. |
[6] |
D. B. Fuks, Cohomology of Infinite Dimensional Lie Algebras, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986. |
[7] |
H. Glöckner, Differentiable mappings between spaces of sections, 2002. arXiv:1308.1172. |
[8] |
J. Grabowski, A. Kotov and N. Poncin, Geometric structures encoded in the Lie structure of an Atiyah algebroid, Transform. Groups, 16 (2011), 137-160.
doi: 10.1007/s00031-011-9126-9. |
[9] |
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1972. |
[10] |
A. W. Knapp, Lie Groups Beyond an Introduction, Birkhäuser, Boston, first edition, 1996.
doi: 10.1007/978-1-4757-2453-0. |
[11] |
H. B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton University Press, second edition, 1994. |
[12] |
P. B. A. Lecomte, Sur la suite exacte canonique associée à un fibré principal, Bulletin de la S. M. F., 113 (1985), 259-271. |
[13] |
K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, volume 124 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1987.
doi: 10.1017/CBO9780511661839. |
[14] |
I. Moerdijk and J. Mrčun, On integrability of infinitesimal actions, Amer. J. Math., 124 (2002), 567-593.
doi: 10.1353/ajm.2002.0019. |
[15] |
S. Morrison, Classifying Spinor Structures, Master's thesis, University of New South Wales, 2001. |
[16] |
K. C. H. Mackenzie and P. Xu, Integration of Lie bialgebroids, Topology, 39 (2000), 445-467.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
A. Nijenhuis, Theory of the Geometric Object, 1952. Doctoral thesis, Universiteit van Amsterdam. |
[18] |
A. Nijenhuis, Geometric aspects of formal differential operations on tensors fields, In Proc. Internat. Congress Math. 1958, pages 463-469. Cambridge Univ. Press, New York, 1960. |
[19] |
A. Nijenhuis, Natural bundles and their general properties. Geometric objects revisited, In Differential geometry (in honor of Kentaro Yano), pages 317-334. Kinokuniya, Tokyo, 1972. |
[20] |
R. S. Palais and C. L. Terng, Natural bundles have finite order, Topology, 19 (1977), 271-277. |
[21] |
J. Peetre, Réctification (sic) à l'article «une caractérisation abstraite des opérateurs différentiels», Math. Scand., 8 (1960), 116-120. |
[22] |
J. Pradines, Théorie de Lie pour les groupoides différentiables, relation entre propriétés locales et globales, Comptes Rendus Acad. Sci. Paris A, 263 (1966), 907-910. |
[23] |
S. E. Salvioli, On the theory of geometric objects, J. Diff. Geom., 7 (1972), 257-278. |
[24] |
J. A. Schouten and J. Haantjes, On the Theory of the Geometric Object, Proc. London Math. Soc., S2-42 (1937), 356-376.
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), 468-472.
doi: 10.1090/S0002-9939-1954-0064764-3. |
[26] |
Kōji Shiga and Toru Tsujishita, Differential representations of vector fields, Kōdai Math. Sem. Rep., 28 (1976/77), 214-225. |
[27] |
F. Takens, Derivations of vector fields, Comp. Math., 26 (1973), 151-158. |
[28] |
C. L. Terng, Natural vector bundles and natural differential operators, Am. J. Math., 100 (1978), 775-828.
doi: 10.2307/2373910. |
[29] |
A. Wundheiler, Objekte, Invarianten und Klassifikation der Geometrie, Abh. Sem. Vektor Tenzoranal. Moskau, 4 (1937), 366-375. |
[1] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[2] |
José F. Cariñena, Irina Gheorghiu, Eduardo Martínez. Jacobi fields for second-order differential equations on Lie algebroids. Conference Publications, 2015, 2015 (special) : 213-222. doi: 10.3934/proc.2015.0213 |
[3] |
Meera G. Mainkar, Cynthia E. Will. Examples of Anosov Lie algebras. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 39-52. doi: 10.3934/dcds.2007.18.39 |
[4] |
Hongliang Chang, Yin Chen, Runxuan Zhang. A generalization on derivations of Lie algebras. Electronic Research Archive, 2021, 29 (3) : 2457-2473. doi: 10.3934/era.2020124 |
[5] |
Jorge Cortés, Manuel de León, Juan Carlos Marrero, Eduardo Martínez. Nonholonomic Lagrangian systems on Lie algebroids. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 213-271. doi: 10.3934/dcds.2009.24.213 |
[6] |
Dennise García-Beltrán, José A. Vallejo, Yurii Vorobiev. Lie algebroids generated by cohomology operators. Journal of Geometric Mechanics, 2015, 7 (3) : 295-315. doi: 10.3934/jgm.2015.7.295 |
[7] |
Javier Pérez Álvarez. Invariant structures on Lie groups. Journal of Geometric Mechanics, 2020, 12 (2) : 141-148. doi: 10.3934/jgm.2020007 |
[8] |
Oǧul Esen, Hasan Gümral. Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields. Journal of Geometric Mechanics, 2012, 4 (3) : 239-269. doi: 10.3934/jgm.2012.4.239 |
[9] |
Giulia Cavagnari, Antonio Marigonda. Measure-theoretic Lie brackets for nonsmooth vector fields. Discrete and Continuous Dynamical Systems - S, 2018, 11 (5) : 845-864. doi: 10.3934/dcdss.2018052 |
[10] |
Davi Obata. Symmetries of vector fields: The diffeomorphism centralizer. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4943-4957. doi: 10.3934/dcds.2021063 |
[11] |
Franz W. Kamber and Peter W. Michor. Completing Lie algebra actions to Lie group actions. Electronic Research Announcements, 2004, 10: 1-10. |
[12] |
Tracy L. Payne. Anosov automorphisms of nilpotent Lie algebras. Journal of Modern Dynamics, 2009, 3 (1) : 121-158. doi: 10.3934/jmd.2009.3.121 |
[13] |
K. C. H. Mackenzie. Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids. Electronic Research Announcements, 1998, 4: 74-87. |
[14] |
Eduardo Martínez. Classical field theory on Lie algebroids: Multisymplectic formalism. Journal of Geometric Mechanics, 2018, 10 (1) : 93-138. doi: 10.3934/jgm.2018004 |
[15] |
Eduardo Martínez. Higher-order variational calculus on Lie algebroids. Journal of Geometric Mechanics, 2015, 7 (1) : 81-108. doi: 10.3934/jgm.2015.7.81 |
[16] |
Madeleine Jotz Lean, Kirill C. H. Mackenzie. Transitive double Lie algebroids via core diagrams. Journal of Geometric Mechanics, 2021, 13 (3) : 403-457. doi: 10.3934/jgm.2021023 |
[17] |
Johannes Huebschmann. On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras. Journal of Geometric Mechanics, 2021, 13 (3) : 385-402. doi: 10.3934/jgm.2021009 |
[18] |
Katarzyna Grabowska, Marcin Zając. The Tulczyjew triple in mechanics on a Lie group. Journal of Geometric Mechanics, 2016, 8 (4) : 413-435. doi: 10.3934/jgm.2016014 |
[19] |
Robert L. Griess Jr., Ching Hung Lam. Groups of Lie type, vertex algebras, and modular moonshine. Electronic Research Announcements, 2014, 21: 167-176. doi: 10.3934/era.2014.21.167 |
[20] |
Mohammad Shafiee. The 2-plectic structures induced by the Lie bialgebras. Journal of Geometric Mechanics, 2017, 9 (1) : 83-90. doi: 10.3934/jgm.2017003 |
2021 Impact Factor: 0.737
Tools
Metrics
Other articles
by authors
[Back to Top]