On Maximal Diagonalizable Lie Subalgebras of the First Hochschild Cohomology
| Autor: | Patrick Le Meur |
|---|---|
| Přispěvatelé: | Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2010 |
| Předmět: |
groupe fondamental
Pure mathematics Monomial Fundamental group 16G10 Algebra and Number Theory [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] Group (mathematics) Quiver Diagonalizable matrix présentation admissible cohomologie de Hochschild 16. Peace & justice Cohomology Ground field sous-algèbre diagonalisable FOS: Mathematics Representation Theory (math.RT) Algebraically closed field Mathematics - Representation Theory algèbre de Lie Mathematics |
| Zdroj: | Communications in Algebra Communications in Algebra, Taylor & Francis, 2010, 38 (4), pp.1325--1340. ⟨10.1080/00927870902915798⟩ |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927870902915798 |
| Popis: | Let A be a basic connected finite dimensional algebra over an algebraically closed field k and with ordinary quiver Q without oriented cycle. To any presentation of A by quiver and admissible relations, Martinez-Villa and de La Pena have associated the fundamental group of the presentation. Assem and de La Pena have constructed an injective mapping from the additive characters of this fundamental group (with values in the ground field) to the first Hochschild cohomology group HH^1(A). We study the image of these mappings associated to the different presentations of A in terms of diagonalizable Lie subalgebras of HH^1(A). Then we characterise the maximal diagonalisable subalgebras of HH^1(A) when A is monomial and Q has no multiple arrows and also when car(k)=0 and Q has no double bypass. Comment: The title was changed to better fit the objectives of the text and the introduction was changed accordingly. Typos were corrected |
| Databáze: | OpenAIRE |
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