A proof of Solomon's second conjecture on local zeta functions of orders

DOI10.1016/S0021-8693(02)00548-3zbMath1025.16011WikidataQ123165214 ScholiaQ123165214MaRDI QIDQ1867302

Osamu Iyama

Publication date: 2 April 2003

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

determinantsAuslander-Reiten quiverszeta functionshereditary ordersorders in semisimple algebrasindecomposable latticesrepresentation finite orderssubmodules of finite index

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Algebras and orders, and their zeta functions (11S45)

Related Items (4)

On Hall Algebras of Hereditary Orders ⋮ Finiteness of representation dimension ⋮ The relationship between homological properties and representation theoretic realization of artin algebras ⋮ Triads.

Cites Work

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• Solomon's second conjecture: A proof for local hereditary orders in central simple algebras
• Zeta functions and composition factors for arithmetic orders
• Algebraic stratification in representation categories
• Zeta functions of arithmetic orders and Solomon's conjectures
• Zeta functions and integral representation theory
• Global dimension two orders are quasi-hereditary
• The prime ideal theorem in non-commutative arithmetic
• New asymptotic formulas for the distribution of left ideals of orders.
• Auslander Algebras as Quasi-Hereditary Algebras
• Finiteness of representation dimension

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