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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 3, Pages 15–22 (Mi ivm6707)  
Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras

A. V. Leont'ev

University of Pereslavl, Pereslavl-Zalessky, Yaroslavl region, Russia
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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.
Keywords: nilpotent Lie algebras, solvable Lie algebras, exact algebraic algorithms, algebraic complexity, tensor rank, lower bounds.
Received: 28.11.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 3, Pages 12–18
DOI: https://doi.org/10.3103/S1066369X10030035
Bibliographic databases:
UDC: 512.55
Language: Russian
Citation: A. V. Leont'ev, “Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 3, 15–22; Russian Math. (Iz. VUZ), 54:3 (2010), 12–18
Citation in format AMSBIB
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\paper Lower bounds for algebraic algorithms for nilpotent and solvable Lie algebras
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\yr 2010
\issue 3
\pages 15--22
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\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 3
\pages 12--18
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