A note on Lie algebra cohomology
| Autor: | Michael Larsen, Valery A. Lunts |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Commutative Algebra Mathematics::Rings and Algebras 010102 general mathematics Lie algebra cohomology Universal enveloping algebra 01 natural sciences Cohomology Mathematics - Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences Lie algebra FOS: Mathematics Equivariant map 010307 mathematical physics 0101 mathematics Mathematics::Representation Theory Algebraic Geometry (math.AG) Augmentation ideal Mathematics |
| Zdroj: | Algebra & Number Theory. 15:773-783 |
| ISSN: | 1944-7833 1937-0652 |
| DOI: | 10.2140/ant.2021.15.773 |
| Popis: | Given a finite dimensional Lie algebra $L$ let $I$ be the augmentation ideal in the universal enveloping algebra $U(L)$. We study the conditions on $L$ under which the $Ext$-groups $Ext (k,k)$ for the trivial $L$-module $k$ are the same when computed in the category of all $U(L)$-modules or in the category of $I$-torsion $U(L)$-modules. We also prove that the Rees algebra $\oplus _{n\geq 0}I^n$ is Noetherian if and only if $L$ is nilpotent. An application to cohomology of equivariant sheaves is given. Comment: Comments are welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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