Derived Localisation in Algebra and Homotopy Theory

Lead Research Organisation: City, University of London
Department Name: Sch of Engineering and Mathematical Sci

Abstract

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Publications

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Angeleri Hügel L (2019) Model Theory of Modules, Algebras and Categories

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Angeleri Hügel L (2020) Flat ring epimorphisms and universal localizations of commutative rings in The Quarterly Journal of Mathematics

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Angeleri Hügel L (2019) Partial silting objects and smashing subcategories in Mathematische Zeitschrift

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Angeleri Hügel L (2017) Torsion pairs in silting theory in Pacific Journal of Mathematics

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Braun C (2018) Derived localisation of algebras and modules in Advances in Mathematics

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Chuang J (2020) Homological epimorphisms, homotopy epimorphisms and acyclic maps in Forum Mathematicum

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Chuang J (2021) Maurer-Cartan Moduli and Theorems of Riemann-Hilbert Type in Applied Categorical Structures

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Chuang J (2021) Homotopy theory of monoids and derived localization in Journal of Homotopy and Related Structures

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Chuang J (2019) On the perturbation algebra in Journal of Algebra

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Chuang J (2021) Rank functions on triangulated categories in Journal für die reine und angewandte Mathematik (Crelles Journal)

 
Description A theory of derived rank functions has been developed, generalising the work of Cohn and Schofield, with connections to derived localisations. A prepirnt has been posted on the ArXiv and further work is in progress. A new approach to the Homological Perturbation Lemma has been introduced. This work, entitled `On the Perturbation Algebra' has been published in the Journal of Algebra. Further works `Maurer-Cartan moduli and theorems of Riemann-Hilbert type' and `Homotopy theory of monoids and derived localization' have been published in Applied Categorical Structures and in Journal of Homotopy and Related Structures. Postdoc Vitoria and collaborators have carried out research on `Torsion Pairs in Silting Theory', published in the Pacific Journal of Mathematics, `Silting and cosilting classes in derived categories', published in the Journal of Algebra, `Realisation functors in tilting theory', published in Mathematische Zeitschrift, `Properties of abelian categories via recollements', published in the Journal of Pure and Applied Mathematics, `A characterisation of t-tilting finite algebras', published in Comtemporary Mathematics, and Definability and Approximations in Triangulated Categories, to be published in Pacific Journal of Mathematics.
Exploitation Route The findings contribute to the academic sphere.
Sectors Other
 
Description The proposed research project belongs to the realm of pure mathematics. As such, it is expected to have impact within the academic community only, at least in the foreseeable future.
First Year Of Impact 2016
Sector Other
 
Description Rank functions on triangulated categories, homotopy theory and representations of finite groups
Amount £393,338 (GBP)
Funding ID EP/T030771/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 03/2021 
End 08/2024