An integral form of the quantized enveloping algebra of sl₂ and its completions

2006/05/11 by Kazuo Habiro, Habiro, Kazuo · 1 citation
Mathematics · #17B37 #57M27 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0605313

openalex publication_date 2006/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce an integral form U of the quantized enveloping algebra of sl₂. The algebra U is just large enough so that the quasi-R-matrix is contained in a completion of U⊗ U. We study several completions of the algebra U, and determine their centers. This study is motivated by a study of integrality properties of the quantum sl₂ invariants of links and integral homology spheres.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Inverted Habiro Series and its Residues

Related

• On the quantum sl₂ invariants of knots and integral homology spheres
• Quantum Lie algebras of type A_n
• Quantized hyperalgebras of rank 1
• Presenting quantum Schur algebras as quotients of the quantized universal enveloping algebra of gl(2)
• Quantum differential operators on the quantum plane