Geodesic
Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 15-22.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain the lower bounds for the tensor rank for the class of nilpotent and solvable Lie algebras (in terms of dimensions of certain quotient algebras). These estimates, in turn, give lower bounds for the complexity of algebraic algorithms for this class of algebras. We adduce examples of attainable estimates for nilpotent Lie algebras of various dimensions.
Keywords: nilpotent Lie algebras, exact algebraic algorithms, algebraic complexity, tensor rank, lower bounds.
Mots-clés : solvable Lie algebras 
@article{IVM_2010_3_a2,
     author = {A. V. Leont'ev},
     title = {Lower bounds for algebraic algorithms for nilpotent and solvable {Lie} algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--22},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_3_a2/}
}
TY  - JOUR
AU  - A. V. Leont'ev
TI  - Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 15
EP  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_3_a2/
LA  - ru
ID  - IVM_2010_3_a2
ER  - 
%0 Journal Article
%A A. V. Leont'ev
%T Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 15-22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_3_a2/
%G ru
%F IVM_2010_3_a2
A. V. Leont'ev. Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 15-22. http://geodesic.mathdoc.fr/item/IVM_2010_3_a2/

[1] Alder A., Strassen V., “On the algorithmic complexity of the associative algebras”, Theor. Comp. Sci., 15:2 (1981), 201–211 | DOI | MR | Zbl

[2] Zhoshina S. A., “O multiplikativnoi slozhnosti algebr Li”, Vestn. Mosk. Un-ta. Ser. 1. Matematika. Mekhanika, 1990, no. 4, 75–77 | MR | Zbl

[3] Zhoshina S. A., “O multiplikativnoi slozhnosti prostykh algebr Li $G_2$, $F_4$, $E_6$, $E_7$, $E_8$ i poluprostykh algebr Li”, Vestn. Mosk. Un-ta. Ser. 1. Matematika. Mekhanika, 1993, no. 4, 35–37 | MR | Zbl

[4] Leontev A. V., “Nizhnie otsenki algebraicheskoi slozhnosti dlya klassicheskikh prostykh algebr Li”, Matem. sb., 199:5 (2008), 27–34 | MR | Zbl

[5] Latyshev V. N., Kombinatornaya teoriya kolets. Slozhnost algebraicheskikh algoritmov, Izd-vo Mosk. un-ta, M., 1987, 105 pp. | MR | Zbl