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Jahresbericht der Deutschen Mathematiker-Vereinigung

Cohomology of Leibniz Algebras

  • 11-10-2023
  • Survey Article
Published in:
Author
Friedrich Wagemann
Published in
Jahresbericht der Deutschen Mathematiker-Vereinigung | Issue 4/2023

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Abstract

The article explores the cohomology of Leibniz algebras, which were introduced to explain the absence of periodicity in algebraic K-theory. Leibniz algebras are vector spaces with a bracket operation that satisfies certain conditions, and their cohomology is defined similarly to Lie algebra cohomology. The article discusses the motivation for studying Leibniz cohomology, its relation to the failure of periodicity in algebraic K-theory, and its applications in understanding the structure of Leibniz algebras. It also presents new results and conjectures in the field, and discusses the relationship between Leibniz cohomology and Lie algebra cohomology. The article is aimed at mathematicians and researchers interested in Lie algebra theory and cohomology, and provides a valuable resource for those working in the field.
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previous article Mathematical Reflections on Locality
Title
Cohomology of Leibniz Algebras
Author
Friedrich Wagemann
Publication date
11-10-2023
Publisher
Springer Berlin Heidelberg
Published in
Jahresbericht der Deutschen Mathematiker-Vereinigung / Issue 4/2023
Print ISSN: 0012-0456
Electronic ISSN: 1869-7135
DOI
https://doi.org/10.1365/s13291-023-00272-0
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