Supertropical

Zur Izhakian; Adi Niv; Louis Rowen

doi:10.1080/03081087.2017.1363148

Supertropical

Zur Izhakian, Adi Niv, Louis Rowen

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version SLS_n of the special linear group SL_n, which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of SLS_n. We also study the monoid generated by SLS_n and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on SLS_n, which enables one to connect different matrices in SLS_n, 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
DOIs	https://doi.org/10.1080/03081087.2017.1363148
State	Published - 3 Jul 2018

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1080/03081087.2017.1363148

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title = "Supertropical",

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

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

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

note = "Publisher Copyright: {\textcopyright} 2017 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2018",

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doi = "10.1080/03081087.2017.1363148",

language = "الإنجليزيّة",

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TY - JOUR

T1 - Supertropical

AU - Izhakian, Zur

AU - Niv, Adi

AU - Rowen, Louis

PY - 2018/7/3

Y1 - 2018/7/3

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

KW - Supertropical matrix algebra

KW - elementary matrix

KW - matrix monoid

KW - quasi-identity

KW - special linear monoid

KW - tropical adjoint matrix

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U2 - 10.1080/03081087.2017.1363148

DO - 10.1080/03081087.2017.1363148

M3 - مقالة

SN - 0308-1087

VL - 66

SP - 1461

EP - 1483

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 7

ER -

Supertropical

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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