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PreprintarXiv licencearXiv

Representation and Extending structure of a Multiplicative Lie algebra

  • Neeraj Kumar Maurya
  • Sumit Kumar Upadhyay
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Abstract

In this paper, we attempt to develop a general notion of representation theory for multiplicative Lie algebras. Consequently, we study equivalent, irreducible, and completely reducible representations. We also introduce the notion of the action of a multiplicative Lie algebra on a vector space and show that there is a one-to-one correspondence between the action and the representation. We also studied the extended structure of a multiplicative Lie algebra through a group.

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Cite

BibTeXRIS
BibTeX
@misc{maurya2026representation,
  title = {{Representation and Extending structure of a Multiplicative Lie algebra}},
  author = {Neeraj Kumar Maurya and Sumit Kumar Upadhyay},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07359},
  eprint = {2609.07359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07359},
}
RIS
TY  - UNPB
TI  - Representation and Extending structure of a Multiplicative Lie algebra
AU  - Neeraj Kumar Maurya
AU  - Sumit Kumar Upadhyay
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07359
UR  - https://arxiv.org/abs/2609.07359
AB  - In this paper, we attempt to develop a general notion of representation theory for multiplicative Lie algebras. Consequently, we study equivalent, irreducible, and completely reducible representations. We also introduce the notion of the action of a multiplicative Lie algebra on a vector space and show that there is a one-to-one correspondence between the action and the representation. We also studied the extended structure of a multiplicative Lie algebra through a group.
ER  -