Geodesic
On the algebra of the Möbius crown
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 149-156 
S. S. Podkorytov. On the algebra of the Möbius crown. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 149-156. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a10/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A commutative algebra over a field gives rise to a representation of the category of finite sets and surjective maps. We consider the restriction of this representation to the subcategory of sets of cardinality at most $r$. For each $r$, we present two non-isomorphic algebras that give rise to isomorphic representations of this subcategory.

[1] S. S. Podkorytov, “Kommutativnye algebry i predstavleniya kategorii konechnykh mnozhestv”, Zap. nauch. semin. POMI, 388, 2011, 189–195

[2] W. Dreckmann, Linearization reflects isomorphism, preprint, 2012 https://www.idmp.uni-hannover.de/fileadmin/institut/IDMP-Studium-Mathematik/downloads/Dreckmann/lincat.pdf

[3] J. Gubeladze, “The isomorphism problem for commutative monoid rings”, J. Pure Appl. Algebra, 129 (1998), 35–65 | DOI | MR | Zbl

[4] J.-L. Loday, Cyclic homology, Springer-Verlag, 1992 | MR | Zbl