Excision and idealization of a multiplicative Lie algebra
Neeraj Kumar Maurya, Amit Kumar, Sumit Kumar Upadhyay
TL;DR
This work introduces excision and idealization constructions for multiplicative Lie algebras and their Lie-algebra analogues, providing explicit algebraic recipes to generate new structures from a given algebra and an ideal. It establishes when the two constructions are isomorphic, analyzes the structure of ideals generated by these processes, and extends the framework by iterating the construction and interpreting excision via fiber products. The results yield concrete invariants and relationships among centers, derived subalgebras, and centers-like objects, while preserving nilpotent and solvable properties under suitable conditions. Together, these developments supply new tools for building, comparing, and classifying multiplicative Lie algebras and Lie algebras of prescribed size or dimension, with potential applications to classification questions and structural analysis.
Abstract
In this article, we introduce the concepts of excision and idealization for a multiplicative Lie algebra (also for a Lie algebra), which provides two new multiplicative Lie algebras (or Lie algebras) from a given multiplicative Lie algebra (or Lie algebra) and an ideal, under certain conditions. These concepts may assist in classifying all multiplicative Lie algebras (or Lie algebras) of a specified order (or dimension).