Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Rings and Algebras

arXiv:0710.0121 (math)
[Submitted on 1 Oct 2007]

Title:On Isomorphism Classes and Invariants of Low Dimensional Complex Filiform Leibniz Algebras (PART 1)

Authors:I.S. Rakhimov, S.K. Said Husain
View PDF
Abstract: The paper aims to investigate the classification problem of low dimensional complex none Lie filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded none Lie filiform Leibniz algebras and the another one is the naturally graded filiform Lie algebras. Here we do consider Leibniz algebras appearing from the naturally graded none Lie filiform Leibniz algebras. This class can be splited into two subclasses. However, isomorphisms within each class there were not investigated. Before this http URL and this http URL suggested an approach to the isomorphism problem in terms of invariants. This paper presents an implementation of their result in low dimensional cases. Here we give the complete classification of complex none Lie filiform Leibniz algebras in dimensions at most 8 from the first class of the above mentioned result and give a hypothetic formula for the number of isomorphism classes in finite dimensional case.
Subjects: Rings and Algebras (math.RA); Algebraic Geometry (math.AG)
MSC classes: 17A32; 17B30
Cite as: arXiv:0710.0121 [math.RA]
  (or arXiv:0710.0121v1 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.0710.0121

Submission history

From: Isamiddin Rakhimov Dr. [view email]
[v1] Mon, 1 Oct 2007 10:04:34 UTC (10 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.RA
< prev   |   next >
new | recent | 2007-10
Change to browse by:
math
math.AG

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)