Resolving by a free action linear category and applications to Hochschild-Mitchell (co)homology

Autor(es)

Cibils, Claude ^[1] ; Marcos, Eduardo N. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, IMAG, Montpellier - France

^[2] Univ Sao Paulo, Dept Matemat, IME, Rua Matao 1010 Cx Pt 20570, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 591, p. 117-141, FEB 1 2022.
• Citações Web of Science: 0

Resumo

Let G be a group acting on a small category Cover a field k, that is C is a G-k-category. We first obtain an unexpected result: C is resolvable by a category which is G-k-equivalent to it, on which G acts freely on objects. This resolving category enables to show that if the coinvariants and the invariants functors are exact, then the coinvariants and invariants of the Hochschild-Mitchell (co)homology of C are isomorphic to the trivial component of the Hochschild-Mitchell (co)homology of the skew category C{[}G]. If the action of G is free on objects, then there is a canonical decomposition of the Hochschild-Mitchell (co)homology of the quotient category C/G along the conjugacy classes of G. This way we provide a general frame for monomorphisms which have been described previously in low degrees. (c) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático