The Grothendieck and Picard groups of finite rank torsion free \(\mathfrak{sl}(2)\)-modules

DOI10.1007/s13398-022-01224-6OpenAlexW3163522409MaRDI QIDQ2121675

Carlos Tejero Prieto, Francisco Jose Plaza Martín

Publication date: 4 April 2022

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-022-01224-6

zbMATH Keywords

Grothendieck group-Picard grouprational \(\mathfrak{sl}(2)\)-modulestorsion free \(\mathfrak{sl}(2)\)-modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Grothendieck groups (category-theoretic aspects) (18F30)

Cites Work

• Construction of simple non-weight \(\mathfrak{sl}(2)\)-modules of arbitrary rank
• Classification of simple sl(2)-modules and finite-dimensionality of the module of extensions of simple sl(2)-modules
• Krull-Schmidt categories and projective covers
• The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
• Extending representations of \(\mathfrak {sl}(2)\) to Witt and Virasoro algebras
• Exact categories
• On the Krull-Schmidt theorem with application to sheaves
• Symmetry, Representations, and Invariants
• Tensor Categories
• On the Endomorphism Ring of a Simple Module Over an Enveloping Algebra
• A survey of integral representation theory
• Algebraic \(K\)-theory
• Picard groups, Grothendieck rings, and Burnside rings of categories
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