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• # Artykuł - szczegóły

## Colloquium Mathematicum

2001 | 89 | 1 | 7-42

## Differentiation and splitting for lattices over orders

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.

7-42

wydano
2001

### Twórcy

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