Contramodules

0555864 - MÚ 2023 RIV SG eng J - Journal Article
Positselski, Leonid
Contramodules.
Confluentes Mathematici. Roč. 13, č. 2 (2021), s. 93-182. ISSN 1793-7442
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : contramodules over coalgebras * topological rings * Tate Harish-Chandra pairs
OECD category: Pure mathematics
Method of publishing: Limited access
https://doi.org/10.5802/cml.78

Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras over commutative rings, contramodules experience a small renaissance now after being all but forgotten for three decades between 1970-2000. Here we present a review of various definitions and results related to contramodules (drawing mostly from our monographs and preprints arXiv:0708.3398, arXiv:0905.2621, arXiv:1202.2697, arXiv:1209.2995, arXiv:1512.08119, arXiv:1710.02230, arXiv:1705.04960, arXiv:1808.00937) - including contramodules over corings, topological associative rings, topological Lie algebras and topological groups, semicontramodules over semialgebras, and a 'contra version' of the Bernstein-Gelfand-Gelfand category O. Several underived manifestations of the comodule-contramodule correspondence phenomenon are discussed.
Permanent Link: http://hdl.handle.net/11104/0330323