Isomorphic Loday functors of non-homeomorphic spaces

2025/12/19 by Igor Baskov, Baskov, Igor
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.17618

openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28

Abstract

Each commutative algebra A gives rise to a representation L_A, which we call the Loday functor of A, of the category Ω of finite sets and surjective maps. In this paper we present two (infinite-dimensional) non-isomorphic algebras over ℂ with isomorphic Loday functors -- the algebras of continuous functions on the Möbius strip and on the cylinder.

Citations

• Commutative algebras and representations of the category of finite sets

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