The minimal realization from deformation theory

DOI10.1006/jabr.1997.7349zbMath0908.17006OpenAlexW2070636491MaRDI QIDQ1271007

Alexander Braverman, Anthony Joseph

Publication date: 14 March 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7349

zbMATH Keywords

enveloping algebraKoszul algebraprimitive idealgraded idealminimal nilpotent orbitGerstenhaber deformationBGG variety

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Universal enveloping algebras of Lie algebras (16S30)

Related Items

The Joseph Ideal for $$\mathfrak {sl}(m|n)$$ ⋮ Notes on higher-spin algebras: minimal representations and structure constants ⋮ Deformation quantization on the closure of minimal coadjoint orbits ⋮ Representation theory in complex rank. II ⋮ Classification of minimal representations of real simple Lie groups ⋮ Notes on super Killing tensors ⋮ Some Properties of Orbital Varieties in Extremal Nilpotent Orbits ⋮ On the existence of smooth orbital varieties in simple Lie algebras ⋮ Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras ⋮ Orbital varieties of the minimal orbit ⋮ Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the variety of a highest weight module
• Über Schichten halbeinfacher Lie-Algebren
• Definition einer Dixmier-Abbildung für \(\mathfrak{sl}(n,\mathbb C)\)
• Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• Constructions of the Weil representations of certain simple Lie algebras
• Minimal realizations and spectrum generating algebras
• Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type
• An intrinsic analysis of unitarizable highest weight modules
• Rings of differential operators on classical rings of invariants
• The Analytic Continuation of the Discrete Series. II
• Annihilators and associated varieties of unitary highest weight modules
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• Frobenius Splitting of Schubert Varieties and Linear Syzygies
• Koszul Duality Patterns in Representation Theory