Differentiation and splitting for lattices over orders

• Autorzy: Wolfgang Rump
• Języki publikacji: EN

Abstrakty

EN

We extend our module-theoretic approach to Zavadskiĭ's differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories $∂̃_{u}:Λ-lat/[ℋ ] ⭇ δ_{u}Λ-lat/[B]$ which generalizes Zavadskiĭ's algorithms for posets and tiled orders, and Simson's reduction algorithm for vector space categories. In this article we replace u by a more general type of monomorphism, and the derived order $δ_{u}Λ$ by some over-order $∂_{u}Λ ⊃ δ_{u}Λ$. Then $∂̃_{u}$ remains an equivalence if $δ_{u}Λ-lat$ is replaced by a certain subcategory of $∂_{u}Λ-lat$. The extended differentiation comprises a splitting theorem that implies Simson's splitting theorem for vector space categories.

Kategorie tematyczne

• 16G30: Representations of orders, lattices, algebras over commutative rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 1
• Strony: 7-42

Daty

wydano

2001

Twórcy

autor

Wolfgang Rump

• Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt, Ostenstr. 26-28, D-85071 Eichstätt, Germany

Identyfikatory

DOI

10.4064/cm89-1-2