Normed representations of weight quivers

2025/07/09 by Yu-Zhe Liu, Liu, Yu-Zhe
Mathematics · #16G10 #46M40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.06962

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and B be two tensor rings given by weight quivers. We introduce norms for tensor rings and (A,B)-bimodules, and define an important category \mathscrA^p_ς in this paper whose object is a triple (N,v,δ) given by an (A,B)-bimodule N, a special element v∈ V satisfying some special conditions, and a special (A,B)-homomorphism δ: N^⊕_p 2^{dim A} → N and each morphism (N,v,δ) → (N',v',δ') is given by an (A,B)-homomorphism θ: N→ N' such that θ(v)=v' and δ' θ^⊕ 2^{dim A} = θδ hold. We show that \mathscrA^p_ς has an initial object such that Daniell integration, Bochner integration, Lebesgue integration, Stone--Weierstrass Approximation Theorem, power series expansion, and Fourier series expansion are morphisms in \mathscrA^p_ς starting with this initial object.

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