2015/12/02 by Yadira Valdivieso-Díaz, Valdivieso-Diaz, Yadira
Mathematics · #16G20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 16E40 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 16W99
paper · pdf · doi:10.48550/arxiv.1512.00738
openalex publication_date 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are several examples in which algebraic properties of Jacobian algebras\nfrom (unpunctured) Riemann surfaces can be computed from the geometry of the\nRiemann surface.\n In this work, we compute the dimension of the Hochschild cohomology groups of\nany Jacobian algebra from unpunctured Riemann surfaces. In those expressions\nappear geometric objects of the triangulated surface, namely: the number of\ninternal triangles and certain types of boundaries. Moreover, we give geometric\nconditions on the triangulated surface (S,M, mathbb T) such that the\nGerstenhaber algebra \HH^*(A mathbb T) has non-trivial\nmultiplicative structures.\n We also show that the derived class of Jacobian algebras from an unpunctured\nsurface (S,M) is not always completely determined by the Hochschild\ncohomology.\n