Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Indian Institute of Information Technology Allahabad
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212086790