2013/02/28 by Yang Han, Han, Yang
Chemistry · Mathematics · #16E30 #16G10 #18E30 #18G10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Art #Axial and Atropisomeric Chirality Synthesis #Character (mathematics) #FOS: Mathematics #K-Theory and Homology (math.KT) #Linguistics #Mathematics #Philosophy #Representation Theory (math.RT) #Rings and Algebras (math.RA) #TRACE (psycholinguistics) #math.KT #math.RA #math.RT #msc:16E30 #msc:16G10 #msc:18E30 #msc:18G10
paper · pdf · doi:10.48550/arxiv.1302.7095
published in arXiv (Cornell University) (Cornell University) · 11 pages
arxiv created 2013/02/28 · openalex publication_date 2013/02/28 · arxiv updated 2013/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that Hattori-Stallings trace induces a homomorphism of abelian groups, called Hattori-Stallings character, from the K1-group of endomorphisms of the perfect derived category of an algebra to its zero-th Hochschild homology, which provides a new proof of Igusa-Liu-Paquette Theorem, i.e., the strong no loop conjecture for finite-dimensional elementary algebras, on the level of complexes. Moreover, the Hattori-Stallings traces of projective bimodules and one-sided projective bimodules are studied, which provides another proof of Igusa-Liu-Paquette Theorem on the level of modules.