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Filiform left-symmetric algebras

K Dekimpe and Veerle Ongenae (UGent)
(1999) GEOMETRIAE DEDICATA. 74(2). p.165-199
Author
Organization
Abstract
A left-symmetric algebra is said to be filiform if both natural descending series induced by the product tend to zero, but as slow as possible. This is the analogue of the more common notion for Lie algebras. In this paper, we develop some theoretical aspects of this class of left-symmetric algebras and we also present a classification of them up till dimension 5.
Keywords
LIE-ALGEBRAS, AFFINE STRUCTURES, Lie algebras, filiform LSA structures

Citation

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MLA
Dekimpe, K., and Veerle Ongenae. “Filiform Left-Symmetric Algebras.” GEOMETRIAE DEDICATA, vol. 74, no. 2, 1999, pp. 165–99, doi:10.1023/A:1005004223336.
APA
Dekimpe, K., & Ongenae, V. (1999). Filiform left-symmetric algebras. GEOMETRIAE DEDICATA, 74(2), 165–199. https://doi.org/10.1023/A:1005004223336
Chicago author-date
Dekimpe, K, and Veerle Ongenae. 1999. “Filiform Left-Symmetric Algebras.” GEOMETRIAE DEDICATA 74 (2): 165–99. https://doi.org/10.1023/A:1005004223336.
Chicago author-date (all authors)
Dekimpe, K, and Veerle Ongenae. 1999. “Filiform Left-Symmetric Algebras.” GEOMETRIAE DEDICATA 74 (2): 165–199. doi:10.1023/A:1005004223336.
Vancouver
1.
Dekimpe K, Ongenae V. Filiform left-symmetric algebras. GEOMETRIAE DEDICATA. 1999;74(2):165–99.
IEEE
[1]
K. Dekimpe and V. Ongenae, “Filiform left-symmetric algebras,” GEOMETRIAE DEDICATA, vol. 74, no. 2, pp. 165–199, 1999.
@article{111424,
  abstract     = {{A left-symmetric algebra is said to be filiform if both natural descending series induced by the product tend to zero, but as slow as possible. This is the analogue of the more common notion for Lie algebras. In this paper, we develop some theoretical aspects of this class of left-symmetric algebras and we also present a classification of them up till dimension 5.}},
  author       = {{Dekimpe, K and Ongenae, Veerle}},
  issn         = {{0046-5755}},
  journal      = {{GEOMETRIAE DEDICATA}},
  keywords     = {{LIE-ALGEBRAS,AFFINE STRUCTURES,Lie algebras,filiform LSA structures}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{165--199}},
  title        = {{Filiform left-symmetric algebras}},
  url          = {{http://doi.org/10.1023/A:1005004223336}},
  volume       = {{74}},
  year         = {{1999}},
}
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