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

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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/}
}
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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/