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MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES

Year 2012, Volume: 12 Issue: 12, 75 - 88, 01.12.2012

Louis A. Levy

Abstract

A Lie algebra multiplier parallels the idea of group theory’s Schur
multiplier. This paper classifies the Lie algebra multipliers for all Lie algebras
in the lower central series of strictly upper triangular matrices. Multipliers are
central, so the classification is focused on computing their dimensions. The
calculations are lengthy because balancing various matrix positions plays an
important role in determining these dimensions. The result divides into six
cases and the dimensions are given as polynomials in the size of the matrices
and the position in the lower central series.

Keywords

multiplier Lie algebra multiplier Schur multiplier

Year 2012, Volume: 12 Issue: 12, 75 - 88, 01.12.2012

Louis A. Levy

Abstract

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Details

Other ID JA97KU98PJ
Journal Section Articles
Authors

Louis A. Levy This is me

Publication Date December 1, 2012
Published in Issue Year 2012 Volume: 12 Issue: 12

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APA Levy, L. A. (2012). MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES. International Electronic Journal of Algebra, 12(12), 75-88.
AMA Levy LA. MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES. IEJA. December 2012;12(12):75-88.
Chicago Levy, Louis A. “MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES”. International Electronic Journal of Algebra 12, no. 12 (December 2012): 75-88.
EndNote Levy LA (December 1, 2012) MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES. International Electronic Journal of Algebra 12 12 75–88.
IEEE L. A. Levy, “MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES”, IEJA, vol. 12, no. 12, pp. 75–88, 2012.
ISNAD Levy, Louis A. “MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES”. International Electronic Journal of Algebra 12/12 (December 2012), 75-88.
JAMA Levy LA. MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES. IEJA. 2012;12:75–88.
MLA Levy, Louis A. “MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES”. International Electronic Journal of Algebra, vol. 12, no. 12, 2012, pp. 75-88.
Vancouver Levy LA. MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES. IEJA. 2012;12(12):75-88.