New examples of rank one solvable real rigid Lie algebras possessing a nonvanishing Chevalley cohomology

2018 ◽  
Vol 339 ◽  
pp. 431-440
Author(s):  
J.M. Ancochea Bermúdez ◽  
R. Campoamor-Stursberg ◽  
F. Oviaño García
Keyword(s):  
Lie Algebras ◽  
Rank One

scholarly journals Toral rank one Lie algebras

1988 ◽  
Vol 115 (1) ◽  
pp. 238-250 ◽  
Author(s):  
Georgia Benkart ◽  
J.Marshall Osborn
Keyword(s):  
Lie Algebras ◽  
Rank One ◽  
Toral Rank

SYMMETRIC SPACE TWO-MATRIX MODELS

1992 ◽  
Vol 07 (23) ◽  
pp. 5781-5796
Author(s):  
ARLEN ANDERSON
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Symmetric Space ◽  
Matrix Models ◽  
Explicit Expression ◽  
Lie Algebras ◽  
Spherical Function ◽  
Scaling Limits ◽  
Maximum Order ◽  
Rank One

The radial form of the partition function of a two-matrix model is formally given in terms of a spherical function for matrices representing any Euclidean symmetric space. An explicit expression is obtained by constructing the spherical function by the method of intertwining. The reduction of two-matrix models based on Lie algebras is an elementary application. A model based on the rank one symmetric space isomorphic to RN is less trivial and is treated in detail. This model may be interpreted as an Ising model on a random branched polymer. It has the unusual feature that the maximum order of criticality is different in the planar and double-scaling limits.

scholarly journals Some Features of Rank One Real Solvable Cohomologically Rigid Lie Algebras with a Nilradical Contracting onto the Model Filiform Lie Algebra Qn

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 10 ◽  
Author(s):  
Rutwig Campoamor-Stursberg ◽  
Francisco Oviaño García
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Torus ◽  
Real Rank ◽  
Eigenvalue Spectrum ◽  
Generic Structure ◽  
Cohomology Space ◽  
Solvable Lie Algebras ◽  
Rank One ◽  
Filiform Lie Algebra

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec ( t ) = 1 , k , k + 1 , ⋯ , n + k − 3 , n + 2 k − 3 for k ≥ 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k ≤ 5 , some series of cohomologically rigid algebras for arbitrary values of k are determined.

scholarly journals Solvable Lie Algebras of Derivations of Rank One

2019 ◽  
Vol 2 (0) ◽  
pp. 6-10
Author(s):  
Anatolii Petravchuk ◽  
Kateryna Sysak
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras ◽  
Rank One

Some Remarks Concerning the Invariants of Rank One Solvable Real Lie Algebras

2005 ◽  
Vol 12 (03) ◽  
pp. 497-518 ◽  
Author(s):  
Rutwig Campoamor-Stursberg
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Arbitrary Dimension ◽  
Coadjoint Representation ◽  
Codimension One ◽  
Solvable Lie Algebra ◽  
Solvable Lie Algebras ◽  
Rank One

A corrected and completed list of six dimensional real Lie algebras with five dimensional nilradical is presented. Their invariants for the coadjoint representation are computed and some results on the invariants of solvable Lie algebras in arbitrary dimension whose nilradical has codimension one are also given. Specifically, it is shown that any rank one solvable Lie algebra of dimension n without invariants determines a family of (n+2k)-dimensional algebras with the same property.

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