메뉴 건너뛰기




Volumn 42, Issue 11-12, 2007, Pages 1052-1065

Poincaré-Birkhoff-Witt theorem for Leibniz n-algebras

Author keywords

Gr bner bases; Leibniz n algebra; Poincar Birkhoff Witt theorem; Universal enveloping algebra

Indexed keywords


EID: 35848940289     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2007.05.003     Document Type: Article
Times cited : (12)

References (22)
  • 1
    • 35848964405 scopus 로고    scopus 로고
    • Aymon, M., 1997. Algèbre enveloppante et digèbre enveloppante d'une algèbre de Leibniz. Travail de diplôme. Université de Genève
  • 2
    • 49349125897 scopus 로고
    • The diamond lemma for ring theory
    • Bergman G.M. The diamond lemma for ring theory. Adv. Math. 29 (1978) 178-218
    • (1978) Adv. Math. , vol.29 , pp. 178-218
    • Bergman, G.M.1
  • 4
    • 34250329486 scopus 로고    scopus 로고
    • Trialgebras and Leibniz 3-algebras
    • Casas J.M. Trialgebras and Leibniz 3-algebras. Bol. Soc. Mat. Mexicana 12 2 (2006) 165-178
    • (2006) Bol. Soc. Mat. Mexicana , vol.12 , Issue.2 , pp. 165-178
    • Casas, J.M.1
  • 6
    • 0001067299 scopus 로고    scopus 로고
    • Leibniz and Lie algebra structures for Nambu algebra
    • Daletskii Y.I., and Takhtajan L.A. Leibniz and Lie algebra structures for Nambu algebra. Lett. Math. Phys. 39 (1997) 127-141
    • (1997) Lett. Math. Phys. , vol.39 , pp. 127-141
    • Daletskii, Y.I.1    Takhtajan, L.A.2
  • 7
    • 0000138835 scopus 로고
    • n-Lie algebras
    • Filippov V.T. n-Lie algebras. Sib. Mat. Zh. 26 6 (1985) 126-140
    • (1985) Sib. Mat. Zh. , vol.26 , Issue.6 , pp. 126-140
    • Filippov, V.T.1
  • 8
    • 0009975897 scopus 로고
    • An introduction to noncommutative Gröbner bases
    • Computational Algebra, Marcel Dekker, Inc., New York
    • Green E.L. An introduction to noncommutative Gröbner bases. Computational Algebra. Lect. Notes in Pure and Appl. Math. vol. 151 (1994), Marcel Dekker, Inc., New York 167-190
    • (1994) Lect. Notes in Pure and Appl. Math. , vol.151 , pp. 167-190
    • Green, E.L.1
  • 9
    • 84964450745 scopus 로고    scopus 로고
    • Leibniz algebras associated with foliations
    • Hagiwara Y., and Mizutani T. Leibniz algebras associated with foliations. Kodai Math. J. 25 (2002) 151-165
    • (2002) Kodai Math. J. , vol.25 , pp. 151-165
    • Hagiwara, Y.1    Mizutani, T.2
  • 10
    • 0000741547 scopus 로고
    • Cohomology of Lie triple systems and Lie algebras with involution
    • Harris B. Cohomology of Lie triple systems and Lie algebras with involution. Trans. Amer. Math. Soc. 98 (1961) 148-162
    • (1961) Trans. Amer. Math. Soc. , vol.98 , pp. 148-162
    • Harris, B.1
  • 11
    • 35848943081 scopus 로고    scopus 로고
    • Helton, J.W., Miller, R.L., Stankus, M., 1996. NCAlgebra: A mathematica package for doing noncommuting algebra. Available from: http://math.ucsd.edu/~ncalg
  • 12
    • 0036830038 scopus 로고    scopus 로고
    • On the representation theory of Lie triple systems
    • Hodge T.L., and Parshall B.J. On the representation theory of Lie triple systems. Trans. Amer. Math. Soc. 354 (2002) 4359-4391
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 4359-4391
    • Hodge, T.L.1    Parshall, B.J.2
  • 13
    • 0039756622 scopus 로고    scopus 로고
    • Leibniz algebroid associated with a Nambu-Poisson structure
    • Ibáñez R., de León M., Marrero J.C., and Padrón E. Leibniz algebroid associated with a Nambu-Poisson structure. J. Phys. A 32 (1999) 8129-8144
    • (1999) J. Phys. A , vol.32 , pp. 8129-8144
    • Ibáñez, R.1    de León, M.2    Marrero, J.C.3    Padrón, E.4
  • 14
    • 35848934166 scopus 로고    scopus 로고
    • Insua, M.A., Ladra, M., 2007. Gröbner bases in enveloping algebras of Leibniz algebras. J. Symbolic Comput. (submitted for publication)
  • 15
    • 0000384948 scopus 로고
    • Lie and Jordan triple systems
    • Jacobson N. Lie and Jordan triple systems. Amer. J. Math. 71 (1949) 149-170
    • (1949) Amer. J. Math. , vol.71 , pp. 149-170
    • Jacobson, N.1
  • 16
    • 0035374081 scopus 로고    scopus 로고
    • Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces
    • Kinyon M.K., and Weinstein A. Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces. Amer. J. Math. 123 (2001) 525-550
    • (2001) Amer. J. Math. , vol.123 , pp. 525-550
    • Kinyon, M.K.1    Weinstein, A.2
  • 17
    • 84968517761 scopus 로고
    • A structure theory of Lie triple systems
    • Lister W. A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72 (1952) 217-242
    • (1952) Trans. Amer. Math. Soc. , vol.72 , pp. 217-242
    • Lister, W.1
  • 18
    • 0002390971 scopus 로고
    • Une version non commutative des algèbres de Lie: Les algèbres de Leibniz
    • Loday J.-L. Une version non commutative des algèbres de Lie: Les algèbres de Leibniz. Enseign. Math. 3 (1993) 269-293
    • (1993) Enseign. Math. , vol.3 , pp. 269-293
    • Loday, J.-L.1
  • 19
    • 0010134579 scopus 로고
    • Universal enveloping algebras of Leibniz algebras and (co)homology
    • Loday J.-L., and Pirashvili T. Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296 (1993) 139-158
    • (1993) Math. Ann. , vol.296 , pp. 139-158
    • Loday, J.-L.1    Pirashvili, T.2
  • 20
    • 0028767836 scopus 로고
    • An introduction to commutative and noncommutative Gröbner bases
    • Mora T. An introduction to commutative and noncommutative Gröbner bases. Theoret. Comput. Sci. 134 (1994) 131-173
    • (1994) Theoret. Comput. Sci. , vol.134 , pp. 131-173
    • Mora, T.1
  • 21
    • 35949035760 scopus 로고
    • Generalized Hamiltonian dynamics
    • Nambu Y. Generalized Hamiltonian dynamics. Phys. Rev. D 7 3 (1973) 2405-2412
    • (1973) Phys. Rev. D , vol.7 , Issue.3 , pp. 2405-2412
    • Nambu, Y.1
  • 22
    • 21344477372 scopus 로고
    • On foundation of the generalized Nambu mechanics
    • Takhtajan L. On foundation of the generalized Nambu mechanics. Comm. Math. Phys. 160 (1994) 295-315
    • (1994) Comm. Math. Phys. , vol.160 , pp. 295-315
    • Takhtajan, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.