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Enriched Homological Algebra and Applications
ID 7ky5pvv
ISBN 978-1-4466-8184-8
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Ebook Type: PDF
Copyright and Title
Revise Copyright InformationTitleEnriched Homological Algebra and ApplicationsSubtitle-ISBN978-1-4466-8184-8Imprint/PublisherLulu.comCopyright LicenseAll Rights Reserved - Standard Copyright LicenseCopyright HolderKhvedri InasaridzeCopyright Year2023Contributors
By (author) Khvedri Inasaridze
By (author) Tamaz Kandelaki
By (author) Samik Basu
Ebook Details
Revise Ebook DetailsDescriptionThe originality of our approach to the study of
homological properties of groups and rings consists of the definition
of a new and natural, unexpected action of a discrete group Γ on the classical
chain complexes defining classical homology of a group G and of a
ring R respectively, induced by its given action on the group G and on
the ring R respectively. By taking the homology groups of the tensor
product of the classical chain complex under this action of Γ with the
coefficient group, we have defined new homology and cohomology groups
of Γ-groups and Γ-rings, called Γ-equivariant (co)homology. These new
tools allowed us to extend important homological properties of groups
and rings to the case of Γ-groups and Γ-rings, opening a new direction
in homological algebra that we call Γ-homological algebra. The
recently developed investigation of equivariant cohomological dimensions
is closely related to Γ-homological algebra.Contributor NotesThe contributors are Georgian mathematicians Hvedri Inassaridze, Tamaz Kandelaki, and mathematicians from India Samik Basu, and Surojit GhoshTable of ContentseBook Proposal
Title: Enriched Homological Algebra and Applications
Author: Hvedri Inassaridze
Preface (2 pages)
Chapter I - Equivariant group (co)homology (16 pages) by Hvedri Inassaridze,
Chapter II - Γ- Algebraic K-theory (12 pages) by Hvedri Inassaridze,
Chapter III - Finite and torsion KK-theories (16 pages) by Hvedri Inassaridze
and Tamaz Kandelaki,
Chapter Iv - Algebraic view on KK-theory (33 pages) by Tamaz Kandelaki,
Chapter V – Slice filtration of certain spectra over square-free cyclic groups
(17 pages) by Samik Basu and Surojit Ghosh,
Chapter VI - Non-trivial extensions in equivariant cohomology with constant
coefficients (26 pages) by Samik Basu and Surojit Ghosh
Categories and Keywords
BISAC Main CategoryMATHEMATICS / GeneralBISAC Category 2MATHEMATICS / Algebra / GeneralBISAC Category 3SCIENCE / Physics / Mathematical & ComputationalKeywordsextensions of Γ-groups Hochschild homology, symbol group, Γ-equivariant group (co)homology, homology of crossed Γ-modules., Brendon cohomology, Mackey functorExplicit Content?Any adult audience
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