TY - JOUR
T1 - Supertropical
AU - Izhakian, Zur
AU - Niv, Adi
AU - Rowen, Louis
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
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
UR - http://www.scopus.com/inward/record.url?scp=85027497936&partnerID=8YFLogxK
U2 - 10.1080/03081087.2017.1363148
DO - 10.1080/03081087.2017.1363148
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AN - SCOPUS:85027497936
SN - 0308-1087
VL - 66
SP - 1461
EP - 1483
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
IS - 7
ER -