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 | |
| Publication status | Published - 2018 |
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Keywords
- elementary matrix
- matrix monoid
- quasi-identity
- special linear monoid
- Supertropical matrix algebra
- tropical adjoint matrix
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Supertropical SLn. / Izhakian, Zur; Niv, Adi; Rowen, Louis.
In: Linear and Multilinear Algebra, Vol. 66, No. 7, 2018, p. 1461-1483.Research output: Contribution to journal › Article
}
TY - JOUR
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.
KW - elementary matrix
KW - matrix monoid
KW - quasi-identity
KW - special linear monoid
KW - Supertropical matrix algebra
KW - tropical adjoint matrix
UR - http://www.scopus.com/inward/record.url?scp=85027497936&partnerID=8YFLogxK
U2 - 10.1080/03081087.2017.1363148
DO - 10.1080/03081087.2017.1363148
M3 - Article
VL - 66
SP - 1461
EP - 1483
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 7
ER -