Cohomología de Hochschild y estructura de Gerstenhaber de las álgebras toupie
Supervisor(es): Solotar, Andrea - Lanzilotta, Marcelo
Resumen:
In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A).
| 2015 | |
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Hochschild cohomology Toupie algebras Representaciones de álgebra Álgebras toupie. |
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| Español | |
| Universidad de la República | |
| COLIBRI | |
| http://hdl.handle.net/20.500.12008/9207 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0) |
| Sumario: | In this thesis we compute the Hochschild cohomology H∗(A) of a certain type of algebras calledtoupie algebras, and we describe the Gerstenhaber structure of ⊕1i=0 Hi(A). A quiver Q is called toupie if it has a unique source and a unique sink, and for any other vertex there is exactly one arrow starting at it and exactly one arrow ending at it. The algebra A is toupie if A = kQ/I with Q a toupie quiver and I any admissible ideal. We first construct a minimal projective resolution of A as Ae-module adapting to this case Bardzell’s resolution for monomial algebras. Using this resolution, we compute a k-basis for every cohomology space Hi(A). The structure of H1(A) as a Lie algebra is described in detail as well as the module structure of Hi(A) over H1(A). |
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