Versal deformations of Leibniz algebras
Alice Fialowski (Eotvos Lorand University, Budapest, Hungary), Ashis, Mandal (Indian Statistical Institute, Kolkata, India), Goutam Mukherjee, (Indian Statistical Institute, Kolkata, India)
TL;DR
This paper develops a comprehensive method to construct versal deformations of Leibniz algebras over fields of characteristic zero, enabling the classification of all non-equivalent deformations.
Contribution
It introduces a complete construction of versal deformations for Leibniz algebras, which is unique at the infinitesimal level and captures all possible deformations.
Findings
Constructed a versal deformation for any Leibniz algebra.
Provided a method to classify all non-equivalent deformations.
Ensured the uniqueness of the versal deformation at the infinitesimal level.
Abstract
In this work we consider deformations of Leibniz algebras over a field of characteristic zero. The main problem in deformation theory is to describe all non-equivalent deformations of a given object. We give a method to solve this problem completely, namely work out a construction of a versal deformation for a given Leibniz algebra, which induces all non-equivalent deformations and is unique on the infinitesimal level.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Geometry Research