Integral Geometry on the Octonionic Plane

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509262" target="_blank" >RIV/00216208:11320/25:10509262 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gOF.NJlEfG" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gOF.NJlEfG</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1512/iumj.2025.74.60161" target="_blank" >10.1512/iumj.2025.74.60161</a>

Result language
angličtina
Original language name
Integral Geometry on the Octonionic Plane
Original language description
We describe explicitly the algebra of Spin(9)-invariant, translation-invariant, continuous valuations on the octonionic plane. Specifically, we present a basis in terms of invariant differential forms and determine the Bernig-Fu convolution on this space. The main technical ingredient we introduce is an extension of the invariant theory of the Lie group Spin(7) to the isotropy representation of the action of Spin(9) on the 15-dimensional sphere, reflecting the underlying octonionic structure. As an application, we compute the principal kinematic formula on the octonionic plane and express in our basis certain Spin(9)-invariant valuations introduced previously by Alesker.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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