Centers associated with the Borel subalgebra of certain simple Lie\n algebras

2014/10/08 by Oz Ben-Shimol, Ben-Shimol, Oz
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1410.2278

openalex publication_date 2014/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue the study in Ben-Shimol [1],[2] and consider a Borel subalgebra\n mathfrakb and its nil radical mathfrakn of the simple Lie algebras of\ntypes G₂, F₄, C_n over arbitrary field. Let\n\L\∈ mathfrakn, mathfrakb . We establish here explicit\nrealizations of the center Z(\L) and semi-center Sz(\L)\nof the enveloping algebra, the Poisson center S(\L)^\L\nand Poisson semi-center S(\L)^\L_\si of\nthe symmetric algebra. We describe their structure as commutative rings and\nestablish isomorphisms Z(\L)\≅~S(\L)^\L,\nSz(\L)\≅ S(\L)^\L_\si.\n

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