Cohomology of Lie Algebra Morphism Triples and Some Applications

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-25 DOI:10.1007/s11040-023-09468-3

Apurba Das

引用次数: 0

Abstract

A Lie algebra morphism triple is a triple \((\mathfrak {g}, \mathfrak {h}, \phi )\) consisting of two Lie algebras \(\mathfrak {g}, \mathfrak {h}\) and a Lie algebra homomorphism \(\phi : \mathfrak {g} \rightarrow \mathfrak {h}\). We define representations and cohomology of Lie algebra morphism triples. As applications of our cohomology, we study some aspects of deformations, abelian extensions of Lie algebra morphism triples and classify skeletal sh Lie algebra morphism triples. Finally, we consider the cohomology of Lie group morphism triples and find a relation with the cohomology of Lie algebra morphism triples.

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李代数态射三元组的上同调及其一些应用

李代数态射三重体是由两个李代数\(\mathfrak {g}, \mathfrak {h}\)和一个李代数同态\(\phi : \mathfrak {g} \rightarrow \mathfrak {h}\)组成的三重体\((\mathfrak {g}, \mathfrak {h}, \phi )\)。定义了李代数态射三元组的表示和上同调。作为上同调的应用，我们研究了李代数态射三元组的变形、阿贝尔扩展，并对骨架李代数态射三元组进行了分类。最后，我们考虑了李群态射三元组的上同调，并找到了它们与李代数态射三元组上同调的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.

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