Autotopisms and isotopisms of trilinear alternating forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F12%3A55677" target="_blank" >RIV/60460709:41310/12:55677 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Autotopisms and isotopisms of trilinear alternating forms
Original language description
For a trilinear alternating form $f$ on a vector space $V$ a generalization of the group of automorphisms -- group of autotopisms $Top f$ is introduced. An autotopism of $f$ is a triple $(alpha,beta,gamma)$ of automorphisms of $V$ satisfying $f(v_1,v_2,v_3)=f(alpha(v_1),beta(v_2),gamma(v_3))$ for all $v_iin V$. Basic results concerning this group are presented and it is shown that the subgroup of $Top f$ containing autotopisms with identity in one coordinate has some interesting properties. Moreover, the notion of equivalence of two trilinear alternating forms is generalized in a similar way to isotopy of forms, and a sufficient condition for a form to be equivalent to all of its isotopes is given. This condition is satisfied for any nondegenerate form on a vector space of odd dimension. Examples of forms with both trivial ($Top f=Aut f$) and nontrivial group of autotopisms are presented.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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