Abstract
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.
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References
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Original Russian Text © A.V. Jeont’ev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 15–22.
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Leont’ev, A.V. Lower bounds for algebraic algorithms for nilpotent and solvable lie algebras. Russ Math. 54, 12–18 (2010). https://doi.org/10.3103/S1066369X10030035
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DOI: https://doi.org/10.3103/S1066369X10030035