# Particle-like structure of Lie algebras

@article{Vinogradov2017ParticlelikeSO, title={Particle-like structure of Lie algebras}, author={Alexandre M. Vinogradov}, journal={Journal of Mathematical Physics}, year={2017}, volume={58}, pages={071703} }

If a Lie algebra structure π€ on a vector space is the sum of a family of mutually compatible Lie algebra structures π€iβs, we say that π€ is simply assembled from the π€iβs. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the π€iβs, one obtains a Lie algebra assembled in two steps from π€iβs, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questionsβ¦Β

## 6 Citations

### Particle-like structure of coaxial Lie algebras

- Mathematics
- 2018

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number ofβ¦

### Particle-like, dyx-coaxial and trix-coaxial Lie algebra structures for a multi-dimensional continuous Toda type system

- Mathematics
- 2020

### Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations

- MathematicsJ. Appl. Math.
- 2020

It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

### Lagrangian formalism and Lie group approach for commutative semigroup of differential equations

- Mathematics
- 2019

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate many novel equations. Two independent methods that can be used toβ¦

### Alexandre Mikhailovich Vinogradov

- Physics, MathematicsRussian Mathematical Surveys
- 2020

On 20 September 2019, Alexandre Mikhailovich Vinogradov, a remarkable mathematician and an extraordinary person, passed away. He was born on 18 February 1938 in Novorossiysk. During World War II heβ¦

### A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(β«u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2Γ 2 [185]. 3 [456, 363, 58, 18, 351]. β [238]. 2 [277]. 3 [350]. pβ¦

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