THE ADJOINT GROUP OF RADICAL RINGS AND RELATED QUESTIONS

2011 ◽  
Author(s):  
Ya. P. SYSAK
Keyword(s):  
Adjoint Group

Subgroups of the Adjoint Group of a Radical Ring

1998 ◽  
Vol 50 (1) ◽  
pp. 3-15 ◽  
Author(s):  
B. Amberg ◽  
O. Dickenschied ◽  
YA. P. Sysak
Keyword(s):  
Adjoint Group ◽  
Radical Ring ◽  
Locally Nilpotent ◽  
Finite Subgroups

AbstractIt is shown that the adjoint group R° of an arbitrary radical ring R has a series with abelian factors and that its finite subgroups are nilpotent. Moreover, some criteria for subgroups of R° to be locally nilpotent are given.

scholarly journals PERIODIC FIRST INTEGRALS FOR HAMILTONIAN SYSTEMS OF LIE TYPE

2011 ◽  
Vol 08 (06) ◽  
pp. 1169-1177 ◽  
Author(s):  
RUBEN FLORES ESPINOZA
Keyword(s):  
Hamiltonian Systems ◽  
Nonlinear Oscillator ◽  
Original System ◽  
First Integrals ◽  
Time Dependent ◽  
Existence Problem ◽  
Adjoint Group ◽  
Killing Form ◽  
Modern Physics ◽  
Existence Of Periodic Solutions

In this paper, we study the existence problem of periodic first integrals for periodic Hamiltonian systems of Lie type. From a natural ansatz for time-dependent first integrals, we refer their existence to the existence of periodic solutions for a periodic Euler equation on the Lie algebra associated to the original system. Under different criteria based on properties for the Killing form or on exponential properties for the adjoint group, we prove the existence of Poisson algebras of periodic first integrals for the class of Hamiltonian systems considered. We include an application for a nonlinear oscillator having relevance in some modern physics applications.

scholarly journals Generating Adjoint Groups

2019 ◽  
Vol 62 (3) ◽  
pp. 733-738 ◽  
Author(s):  
Be'eri Greenfeld
Keyword(s):  
Open Problem ◽  
Jacobson Radical ◽  
The Other ◽  
Adjoint Group ◽  
Finitely Generated ◽  
Infinite Dimensional ◽  
Other Hand ◽  
Nil Ring

AbstractWe prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated. We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated and, on the other hand, construct a finitely generated, infinite-dimensional nil algebra whose adjoint group is generated by elements of bounded torsion.

scholarly journals Associative rings with metabelian adjoint group

2004 ◽  
Vol 277 (2) ◽  
pp. 456-473 ◽  
Author(s):  
Bernhard Amberg ◽  
Yaroslav Sysak
Keyword(s):  
Adjoint Group ◽  
Associative Rings

scholarly journals The adjoint group of a Coxeter quandle

2020 ◽  
Vol 60 (4) ◽  
pp. 1245-1260
Author(s):  
Toshiyuki Akita
Keyword(s):  
Adjoint Group

On the Adjoint Group of Semiprime Rings

2006 ◽  
Vol 35 (1) ◽  
pp. 265-270 ◽  
Author(s):  
F. Catino ◽  
M. M. Miccoli ◽  
Ya. P. Sysak
Keyword(s):  
Adjoint Group ◽  
Semiprime Rings

The Dual Pair PGL3 × G2

1997 ◽  
Vol 40 (3) ◽  
pp. 376-384
Author(s):  
Benedict H. Gross ◽  
Gordan Savin
Keyword(s):  
Closed Subgroup ◽  
Dual Pair ◽  
Adjoint Group ◽  
Minimal Representation

AbstractLet H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representation of H to the closed subgroup PGL3 × G2.

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