Special lie algebras with maximality condition for abelian subalgebras

1991 ◽  
Vol 19 (3) ◽  
pp. 863-869 ◽  
Author(s):  
M.V. Zaicev
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras ◽  
Maximality Condition

scholarly journals Maximal abelian subalgebras of complex orthogonal lie algebras

1990 ◽  
Vol 141 ◽  
pp. 183-220 ◽  
Author(s):  
V. Hussin ◽  
P. Winternitz ◽  
H. Zassenhaus
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras

Abelian subalgebras in some particular types of Lie algebras

2009 ◽  
Vol 71 (12) ◽  
pp. e401-e408
Author(s):  
Manuel Ceballos ◽  
Juan Núñez ◽  
Ángel F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras

scholarly journals FAITHFUL REPRESENTATIONS OF MINIMAL DIMENSION OF CURRENT HEISENBERG LIE ALGEBRAS

2009 ◽  
Vol 20 (11) ◽  
pp. 1347-1362 ◽  
Author(s):  
LEANDRO CAGLIERO ◽  
NADINA ROJAS
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Abelian Subalgebras ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Minimal Dimension

Given a Lie algebra 𝔤 over a field of characteristic zero k, let μ(𝔤) = min{dim π : π is a faithful representation of 𝔤}. Let 𝔥m be the Heisenberg Lie algebra of dimension 2m + 1 over k and let k [t] be the polynomial algebra in one variable. Given m ∈ ℕ and p ∈ k [t], let 𝔥m, p = 𝔥m ⊗ k [t]/(p) be the current Lie algebra associated to 𝔥m and k [t]/(p), where (p) is the principal ideal in k [t] generated by p. In this paper we prove that [Formula: see text]. We also prove a result that gives information about the structure of a commuting family of operators on a finite dimensional vector space. From it is derived the well-known theorem of Schur on maximal abelian subalgebras of 𝔤𝔩(n, k ).

Algorithmic method to obtain abelian subalgebras and ideals in Lie algebras

2012 ◽  
Vol 89 (10) ◽  
pp. 1388-1411 ◽  
Author(s):  
Manuel Ceballos ◽  
Juan Núñez ◽  
Ángel F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras ◽  
Algorithmic Method

scholarly journals Maximal abelian subalgebras of pseudoorthogonal lie algebras

1992 ◽  
Vol 173 ◽  
pp. 125-163 ◽  
Author(s):  
V. Hussin ◽  
P. Winternitz ◽  
H. Zassenhaus
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras

Abelian subalgebras on Lie algebras

2015 ◽  
Vol 17 (04) ◽  
pp. 1550050
Author(s):  
Manuel Ceballos ◽  
Juan Núñez ◽  
Ángel F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Current Status ◽  
Historical Evolution ◽  
Open Problems ◽  
Abelian Subalgebras

Abelian subalgebras play an important role in the study of Lie algebras and their properties and structures. In this paper, the historical evolution of this concept is shown, analyzing the current status for the research on this topic. So, the main results obtained from previous years are indicated and commented here. Additionally, a list of some related open problems is also given.

Maximal abelian subalgebras of real and complex symplectic Lie algebras

1983 ◽  
Vol 24 (8) ◽  
pp. 1973-1985 ◽  
Author(s):  
J. Patera ◽  
P. Winternitz ◽  
H. Zassenhaus
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras ◽  
Complex Symplectic

scholarly journals Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z2-graded Lie algebras

2006 ◽  
Vol 207 (1) ◽  
pp. 156-204 ◽  
Author(s):  
Paola Cellini ◽  
Victor G. Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi
Keyword(s):  
Lie Algebras ◽  
Symmetric Spaces ◽  
Graded Lie Algebras ◽  
Abelian Subalgebras

scholarly journals Maximal Abelian subalgebras of pseudounitary lie algebras

1990 ◽  
Vol 135 ◽  
pp. 79-151 ◽  
Author(s):  
M.A. del Olmo ◽  
M.A. Rodríguez ◽  
P. Winternitz ◽  
H. Zassenhaus
Keyword(s):  
Lie Algebras ◽  
Abelian Subalgebras
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