On homology of Lie algebras over commutative rings
| Autor: | Vladislav Romanovskii, Sergei O. Ivanov, Fedor Pavutnitskiy, Anatolii Zaikovskii |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Koszul complex Principal ideal domain K-Theory and Homology (math.KT) Commutative ring Homology (mathematics) 01 natural sciences 0103 physical sciences Lie algebra Mathematics - K-Theory and Homology FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics |
| Popis: | We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over Z , and study connections between them. In particular, we show that they are naturally isomorphic in the case of a Lie algebra which is flat as a module. As an auxiliary result we prove that the Koszul complex of a module M over a principal ideal domain that connects the exterior and the symmetric powers 0 → Λ n M → M ⊗ Λ n − 1 M → … → S n − 1 M ⊗ M → S n M → 0 is purely acyclic. |
| Databáze: | OpenAIRE |
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