Cargando…
Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology /
In this monograph, we extend S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundame...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2016.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1151. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | In this monograph, we extend S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, we show that our construction behaves well with respect to structure preserving functors between exact monoidal categories. We use our main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, we further determine a significant part of the Lie bracket's kernel, and thereby prove a conjecture by L. Menichi. Along the way, we introduce n-extension closed and entirely extension closed subcategories of abelian categories, and study some of their properties. |
|---|---|
| Notas: | "Volume 243, number 1151 (fourth of 4 numbers), September 2016." |
| Descripción Física: | 1 online resource (v, 146 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 141-146). |
| ISBN: | 9781470434502 1470434504 |
| ISSN: | 0065-9266 ; |