Some remarks on invariants

Fuente: arXiv
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Autores principales: Cederwall, Martin, Hutomo, Jessica, Kuzenko, Sergei M., Lechner, Kurt, Sorokin, Dmitri P.
Formato: Preprint
Publicado: 2025
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author Cederwall, Martin
Hutomo, Jessica
Kuzenko, Sergei M.
Lechner, Kurt
Sorokin, Dmitri P.
author_facet Cederwall, Martin
Hutomo, Jessica
Kuzenko, Sergei M.
Lechner, Kurt
Sorokin, Dmitri P.
contents The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In mathematical terms the problem can be formulated as follows. Given a semi-simple finite-dimensional Lie algebra $\mathfrak g$ and a $\mathfrak g$-module $V$, one may ask about the structure of the sub-ring of $\mathfrak g$-invariants inside the ring freely generated by the module. We point out how some information about the ring of invariants may be obtained by studying an extended Lie algebra. Numerous examples are given, with particular focus on the difficult problem of classifying invariants of a self-dual 5-form in 10 dimensions.
format Preprint
id arxiv_https___arxiv_org_abs_2509_14350
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Some remarks on invariants
Cederwall, Martin
Hutomo, Jessica
Kuzenko, Sergei M.
Lechner, Kurt
Sorokin, Dmitri P.
High Energy Physics - Theory
Mathematical Physics
Rings and Algebras
Representation Theory
The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In mathematical terms the problem can be formulated as follows. Given a semi-simple finite-dimensional Lie algebra $\mathfrak g$ and a $\mathfrak g$-module $V$, one may ask about the structure of the sub-ring of $\mathfrak g$-invariants inside the ring freely generated by the module. We point out how some information about the ring of invariants may be obtained by studying an extended Lie algebra. Numerous examples are given, with particular focus on the difficult problem of classifying invariants of a self-dual 5-form in 10 dimensions.
title Some remarks on invariants
topic High Energy Physics - Theory
Mathematical Physics
Rings and Algebras
Representation Theory
url https://arxiv.org/abs/2509.14350