Derived homotopy algebras
- Autores: Jeroen Maes
- Directores de la Tesis: Fernando Muro Jiménez (dir. tes.)
- Lectura: En la Universidad de Sevilla ( España ) en 2016
- Idioma: español
- Número de páginas: 168
- Tribunal Calificador de la Tesis: Carles Casacuberta i Vergés (presid.), Ramón Jesús Flores Díaz (secret.), Andrew Peter Tonks (voc.), Urtzi Buijs Martín (voc.), Marcy Daniel Robertson (voc.)
- Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad de Sevilla
- Materias:
- Enlaces
- Tesis en acceso abierto en: Idus
- Resumen
Derived A-algebras are derived and homotopy invariant versions of differential graded algebras. They were introduced by Steffen Sagave in 20 0 in order to construct minimal models for diferential graded algebras over arbitrary commutative rings. Muriel Livernet, Constanze Roitzheim, and Sarah Whitehouse showed in 2013 how they can be viewed as algebras over the minimal model of the operad encoding bicomplexes with a compatible associative multiplication. We extend their work for the associative operad to a general quadratic Koszul operad O satisfying standard projectivity assumptions. This leads to the new notion of derived homotopy O-algebra, where minimal models for O-algebras are defined. We explicitly compute generating operations and relations when O is the associative operad, the commutative operad, and the operad encoding Lie algebras.
