Finite basis property for the identities of representations of a simple three-dimensional Lie algebra over a field of characteristic zero

1988 ◽  
pp. 101-109
Author(s):  
Yu. P. Razmyslov
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Three Dimensional ◽  
Basis Property ◽  
Finite Basis ◽  
Finite Basis Property ◽  
Algebra Over A Field

FINITELY BASED WORDS

2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR
Keyword(s):  
Sufficient Conditions ◽  
Basis Property ◽  
Free Monoid ◽  
Finite Basis ◽  
Finitely Based ◽  
Finite Basis Property ◽  
Letter Alphabet ◽  
Finite Language ◽  
Rees Quotient ◽  
The Ideal

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

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.

The finite basis property of a certain semigroup of upper triangular matrices over a field

2016 ◽  
Vol 15 (09) ◽  
pp. 1650177 ◽  
Author(s):  
Yuzhu Chen ◽  
Xun Hu ◽  
Yanfeng Luo
Keyword(s):  
Basis Property ◽  
Finite Basis ◽  
Main Diagonal ◽  
Finitely Based ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Finite Basis Property ◽  
Open Question ◽  
Nonfinitely Based ◽  
Secondary Diagonal

Let [Formula: see text] be the semigroup of all upper triangular [Formula: see text] matrices over a field [Formula: see text] whose main diagonal entries are [Formula: see text]s and/or [Formula: see text]s. Volkov proved that [Formula: see text] is nonfinitely based as both a plain semigroup and an involution semigroup under the reflection with respect to the secondary diagonal. In this paper, we shall prove that [Formula: see text] is finitely based for any field [Formula: see text]. When [Formula: see text], this result partially answers an open question posed by Volkov.

scholarly journals Centre-by-metabelian Lie algebras

1973 ◽  
Vol 15 (3) ◽  
pp. 259-264 ◽  
Author(s):  
M. R. Vaughan-Lee
Keyword(s):  
Recent Result ◽  
Lie Algebras ◽  
Basis Property ◽  
Finite Basis ◽  
Metabelian Groups ◽  
Finite Basis Property ◽  
Characteristic 2

If V is a variety of metabelian Lie algebras then V has a finite basis for its laws [3]. The proof of this result is similar to Cohen's proof that varieties of metabelian groups have the finite basis property [1]. However there are centre-by-metabelian Lie algebras of characteristic 2 which do not have a finite basis for their laws [4] this contrasts with McKay's recent result that varieties of centre-by-metabelian groups do have the finite basis property [2]. The rollowing theorem shows that once again “2” is the odd man out.

Finite basis property for certain varieties of algebras

1974 ◽  
Vol 13 (6) ◽  
pp. 394-399 ◽  
Author(s):  
Yu. P. Razmyslov
Keyword(s):  
Basis Property ◽  
Finite Basis ◽  
Finite Basis Property

Palindromes in the free metabelian Lie algebras

2019 ◽  
Vol 29 (05) ◽  
pp. 885-891
Author(s):  
Şehmus Fındık ◽  
Nazar Şahi̇n Öğüşlü
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Reverse Order ◽  
Generating Set ◽  
Linear Basis ◽  
Free Metabelian Lie Algebra ◽  
Definition Of ◽  
Algebra Over A Field

A palindrome, in general, is a word in a fixed alphabet which is preserved when taken in reverse order. Let [Formula: see text] be the free metabelian Lie algebra over a field of characteristic zero generated by [Formula: see text]. We propose the following definition of palindromes in the setting of Lie algebras: An element [Formula: see text] is called a palindrome if it is preserved under the change of generators; i.e. [Formula: see text]. We give a linear basis and an explicit infinite generating set for the Lie subalgebra of palindromes.

scholarly journals A polynomial map preserving the finite basis property

1977 ◽  
Vol 49 (1) ◽  
pp. 154-161 ◽  
Author(s):  
N.S Mendelsohn ◽  
R Padmanabhan
Keyword(s):  
Basis Property ◽  
Finite Basis ◽  
Finite Basis Property ◽  
Polynomial Map
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