Contractions of Lie algebras and algebraic groups

2007/03/23 by Dietrich Burde, Burde, Dietrich · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.math/0703701

openalex publication_date 2007/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.

Cited by

• Group Contractions via Infinite-Dimensional Lie Theory
• On formal deformations and degenerations of evolution algebras

Related

• Degenerations and contractions of algebras and forms
• Separation of variables and Lie algebra contractions. Applications to special functions
• From Wigner--Inönü Group Contraction to Contractions of Algebraic Structures
• Lie algebras : Classification, Deformations and Rigidity
• A comparison of deformations and geometric study of associative algebras varieties