Extending the Search for Symmetries in the Genetic Code

2003 ◽  
Vol 17 (17) ◽  
pp. 3135-3204 ◽  
Author(s):  
Fernando Antoneli ◽  
Lígia Braggion ◽  
Michael Forger ◽  
José Eduardo M. Hornos
Keyword(s):  
Genetic Code ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
Simple Lie Algebras ◽  
Symmetry Breakings

We report on the search for symmetries in the genetic code involving the medium rank simple Lie algebras [Formula: see text] and [Formula: see text], in the context of the algebraic approach originally proposed by one of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution.

LIE-ALGEBRAIC APPROACH TO THE PROBLEM OF QUASI-EXACT SOLUBILITY IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (23) ◽  
pp. 1891-1899 ◽  
Author(s):  
A. G. USHVERIDZE
Keyword(s):  
Quantum Mechanics ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
New Method ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Exactly Solvable

A new method of constructing quasi-exactly solvable models of quantum mechanics is proposed. This method is based on the use of infinite-dimensional representations of simple and semi-simple Lie algebras.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

2010 ◽  
Vol 24 (04) ◽  
pp. 435-463 ◽  
Author(s):  
FERNANDO ANTONELI ◽  
MICHAEL FORGER ◽  
PAOLA A. GAVIRIA ◽  
JOSÉ EDUARDO M. HORNOS
Keyword(s):  
Amino Acid ◽  
Genetic Code ◽  
Lie Groups ◽  
Lie Algebras ◽  
Finite Groups ◽  
Algebraic Approach ◽  
Lie Superalgebras ◽  
Algebraic Models ◽  
Symmetry Principles

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

SYMMETRY AND SYMMETRY BREAKING: AN ALGEBRAIC APPROACH TO THE GENETIC CODE

1999 ◽  
Vol 13 (23) ◽  
pp. 2795-2885 ◽  
Author(s):  
JOSÉ EDUARDO M. HORNOS ◽  
YVONE M. M. HORNOS ◽  
MICHAEL FORGER
Keyword(s):  
Molecular Biology ◽  
Symmetry Breaking ◽  
Representation Theory ◽  
Genetic Code ◽  
Lie Groups ◽  
Algebraic Approach ◽  
General Nature ◽  
Comprehensive Review ◽  
Background Material ◽  
Symmetry Breakings

We give a comprehensive review of the algebraic approach to the genetic code originally proposed by two of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution. We present the relevant background material from molecular biology and from mathematics, including the representation theory of (semi) simple Lie groups/algebras, together with considerations of general nature.

scholarly journals CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS

2019 ◽  
Vol 62 (S1) ◽  
pp. S14-S27 ◽  
Author(s):  
ISABEL CUNHA ◽  
ALBERTO ELDUQUE
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Nonassociative Algebras ◽  
Exceptional Lie Algebras

AbstractThe exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

scholarly journals UNIVERSAL CALABI–YAU ALGEBRA: TOWARDS AN UNIFICATION OF COMPLEX GEOMETRY

2003 ◽  
Vol 18 (30) ◽  
pp. 5541-5612 ◽  
Author(s):  
F. ANSELMO ◽  
J. ELLIS ◽  
D. V. NANOPOULOS ◽  
G. VOLKOV
Keyword(s):  
Lie Algebras ◽  
Complex Geometry ◽  
Algebraic Approach ◽  
Higher Dimensions ◽  
Normal Algebra ◽  
Natural Extensions ◽  
Recurrence Formulae ◽  
Different Dimensions ◽  
Arbitrary Dimensions

We present a universal normal algebra suitable for constructing and classifying Calabi–Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to Batyrev's reflexive polyhedra, and their n-ary combinations. It also includes a "dual" construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi–Yau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of Calabi–Yau spaces in different dimensions, and concrete visualizations of their singularities related to Cartan–Lie algebras. This Universal Calabi–Yau algebra is a powerful tool for deciphering the Calabi–Yau genome in all dimensions.

Models of isotropic simple lie algebras

1979 ◽  
Vol 7 (17) ◽  
pp. 1835-1875 ◽  
Author(s):  
B.N. Allison
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

scholarly journals On the construction of simple lie algebras

1973 ◽  
Vol 27 (1) ◽  
pp. 158-183 ◽  
Author(s):  
S Berman
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras
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