Let k be a field, A a finite-dimensional Frobenius k-algebra and ρ: A → A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A → k. Assume that k has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A0 ⊕ ... ⊕ Am-1 of A, obtained by defining Ai = {a ∈ A : ρ(a) = wia}, and the decomposition HH*(A) = ⊕i=0 m-1 HHi* Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH*(A) = HH0*(A) and that if the decomposition of A is strongly ℤ/mℤ-graded, then ℤ/mℤ acts on HH*(A 0) and HH*(A) = HH0*(A) = HH*(A 0)ℤ/mℤ.
Documento: | Artículo |
Título: | Hochschild cohomology of Frobenius algebras |
Autor: | Guccione, J.A.; Guccione, J.J. |
Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, (1428) Buenos Aires, Argentina |
Año: | 2004 |
Volumen: | 132 |
Número: | 5 |
Página de inicio: | 1241 |
Página de fin: | 1250 |
DOI: | http://dx.doi.org/10.1090/S0002-9939-03-07350-7 |
Título revista: | Proceedings of the American Mathematical Society |
Título revista abreviado: | Proc. Am. Math. Soc. |
ISSN: | 00029939 |
PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029939_v132_n5_p1241_Guccione.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v132_n5_p1241_Guccione |