Supertropical SLn

Zur Izhakian; Adi Niv; Louis Rowen

doi:10.1080/03081087.2017.1363148

Supertropical SLn

Zur Izhakian, Adi Niv^*, Louis Rowen

^*Corresponding author for this work

Research output: Contribution to journal › Article

Abstract

Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.

Original language	English
Pages (from-to)	1461-1483
Number of pages	23
Journal	Linear and Multilinear Algebra
Volume	66
Issue number	7
Early online date	16 Aug 2017
DOIs	https://doi.org/10.1080/03081087.2017.1363148
Publication status	Published - 2018

Keywords

elementary matrix
matrix monoid
quasi-identity
special linear monoid
Supertropical matrix algebra
tropical adjoint matrix

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2017.1363148Licence: Unspecified

https://arxiv.org/abs/1508.04483Licence: Unspecified
Link to publication in Scopus

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Izhakian, Z., Niv, A., & Rowen, L. (2018). Supertropical SLn. Linear and Multilinear Algebra, 66(7), 1461-1483. https://doi.org/10.1080/03081087.2017.1363148

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abstract = "Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on {\textquoteleft}quasi-identity{\textquoteright} matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.",

keywords = "elementary matrix, matrix monoid, quasi-identity, special linear monoid, Supertropical matrix algebra, tropical adjoint matrix",

author = "Zur Izhakian and Adi Niv and Louis Rowen",

note = "The research of the first author has been supported by the Research Councils UK (EPSRC) [grant number EP/N02995X/1]. The second author has been supported by the French Chateaubriand grant and INRIA postdoctoral fellowship.",

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doi = "10.1080/03081087.2017.1363148",

language = "English",

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T1 - Supertropical SLn

AU - Izhakian, Zur

AU - Niv, Adi

AU - Rowen, Louis

N1 - The research of the first author has been supported by the Research Councils UK (EPSRC) [grant number EP/N02995X/1]. The second author has been supported by the French Chateaubriand grant and INRIA postdoctoral fellowship.

PY - 2018

Y1 - 2018

N2 - Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.

AB - Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.

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KW - matrix monoid

KW - quasi-identity

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KW - Supertropical matrix algebra

KW - tropical adjoint matrix

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