The prolongation of central extensions
Nguyen Tien Quang, Che T. Kim Phung, Pham Thi Cuc

TL;DR
This paper develops an obstruction theory and classification method for the prolongation of central extensions using low-dimensional group cohomology, advancing understanding of their structure and properties.
Contribution
It introduces a new framework for studying $(oldsymbol{ extalpha}, oldsymbol{ extgamma})$-prolongations of central extensions, including classification via cohomology.
Findings
Established an obstruction theory for $(oldsymbol{ extalpha}, oldsymbol{ extgamma})$-prolongations.
Classified such prolongations using low-dimensional cohomology groups.
Provided tools for analyzing the structure of extended central groups.
Abstract
The aim of this paper is to study the -prolongation of central extensions. We obtain the obstruction theory for -prolongations and classify -prolongations thanks to low-dimensional cohomology groups of groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Operator Algebra Research
