scholarly journals An integral basis for the universal enveloping algebra of the Onsager algebra

2021 ◽  
pp. 1-24
Author(s):  
Angelo Bianchi ◽  
Samuel Chamberlin
Keyword(s):  
Universal Enveloping Algebra ◽  
Integral Basis ◽  
Enveloping Algebra ◽  
Onsager Algebra

scholarly journals DG Poisson algebra and its universal enveloping algebra

2016 ◽  
Vol 59 (5) ◽  
pp. 849-860 ◽  
Author(s):  
JiaFeng Lü ◽  
XingTing Wang ◽  
GuangBin Zhuang
Keyword(s):  
Poisson Algebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra

scholarly journals ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES

2009 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
JONATHAN BROWN ◽  
JONATHAN BRUNDAN
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Universal Enveloping Algebra ◽  
General Linear ◽  
Enveloping Algebra ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Algebra Over A Field

AbstractWe construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

scholarly journals Free Poisson fields and their automorphisms

2016 ◽  
Vol 15 (10) ◽  
pp. 1650196 ◽  
Author(s):  
Leonid Makar-Limanov ◽  
Ualbai Umirbaev
Keyword(s):  
Universal Enveloping Algebra ◽  
Arbitrary Field ◽  
Group Of Automorphisms ◽  
Cremona Group ◽  
Enveloping Algebra ◽  
Ideal Ring ◽  
Poisson Fields ◽  
Poisson Field

Let [Formula: see text] be an arbitrary field of characteristic [Formula: see text]. We prove that the group of automorphisms of a free Poisson field [Formula: see text] in two variables [Formula: see text] over [Formula: see text] is isomorphic to the Cremona group [Formula: see text]. We also prove that the universal enveloping algebra [Formula: see text] of a free Poisson field [Formula: see text] is a free ideal ring and give a characterization of the Poisson dependence of two elements of [Formula: see text] via universal derivatives.

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