Jacobi-Zariski long nearly exact sequences for associative algebras

Author(s)

Cibils, Claude ^[1] ; Lanzilotta, Marcelo ^[2] ; Marcos, Eduardo N. ^[3] ; Solotar, Andrea ^{[4, 5]}

Affiliation

^[1] Univ Montpellier, CNRS, Inst Montpellierain Alexander Grothendieck, Pl Eugene Bataillon, F-34095 Montpellier - France

^[2] Univ Republica, Inst Matemat & Estadist Rafael Laguardia, Fac Ingn, Julio Herrera y Reissig 565, Montevideo 11300 - Uruguay

^[3] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

^[4] Univ Buenos Aires, CONICET, IMAS, Fac Ciencias Exactas & Nat, Ciudad Univ, Pabellon 1, RA-1428 Buenos Aires, DF - Argentina

^[5] Univ Buenos Aires, Dept Matemat, Ciudad Univ, Pabellon 1, RA-1428 Buenos Aires, DF - Argentina

• Document type: Journal article
• Source: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; v. 53, n. 6, p. 1636-1650, DEC 2021.
• Web of Science Citations: 1

Abstract

For an extension of associative algebras B subset of A over a field and an A-bimodule X, we obtain a Jacobi-Zariski long nearly exact sequence relating the Hochschild homologies of A and B, and the relative Hochschild homology, all of them with coefficients in X. This long sequence is exact twice in three. There is a spectral sequence which converges to the gap of exactness. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants