Centers associated with the Borel subalgebra of the general linear Lie algebra

2014/01/03 by Oz Ben-Shimol, Ben-Shimol, Oz
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1401.0755

openalex publication_date 2014/01/03 · arxiv created 2014/01/04 · arxiv updated 2014/01/07 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

We consider a Borel subalgebra \fg of the general linear algebra and its subalgebra \BB which is a Borel subalgebra of the special linear algebra, over arbitrary field. Let \cL∈\\fg, \BB\. We establish here explicit realizations of the center Z(\cL) and semi-center Sz(\cL) of the enveloping algebra, the Poisson center S(\cL)^\cL and Poisson semi-center S(\cL)^\cL_\si of the symmetric algebra. We describe their structure as commutative rings and establish isomorphisms Z(\cL)≅ S(\cL)^\cL, Sz(\cL)≅ S(\cL)^\cL_\si

Related

• Centers associated with the Borel subalgebra of certain simple Lie algebras
• The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven
• On the semi-centre of a Poisson algebra
• Around the center
• Centers of Universal Enveloping Algebras