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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
n-ary algebras: a review with applications |
Type |
Journal Article |
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Year |
2010 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
43 |
Issue |
29 |
Pages |
293001 - 117pp |
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Keywords |
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Abstract |
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations ( it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A(4) model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. |
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Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Theoret Phys, Fac Phys, E-46100 Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Notes |
ISI:000279463100003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
419 |
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Author |
Botella-Soler, V.; Castelo, J.M.; Oteo, J.A.; Ros, J. |
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Title |
Bifurcations in the Lozi map |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
44 |
Issue |
30 |
Pages |
305101 - 14pp |
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Keywords |
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Abstract |
We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period. |
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Address |
[Botella-Soler, V; Ros, J] Univ Valencia, CSIC, Dept Fis Teor, E-46100 Valencia, Spain, Email: vicente.botella@uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Conference |
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Notes |
WOS:000292386000006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
679 |
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Author |
Botella-Soler, V.; Oteo, J.A.; Ros, J.; Glendinning, P. |
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Title |
Lyapunov exponent and topological entropy plateaus in piecewise linear maps |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
12 |
Pages |
125101 - 26pp |
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Keywords |
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Abstract |
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. |
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Address |
[Botella-Soler, V.] IST Austria, A-3400 Klosterneuburg, Austria, Email: vbsoler@ist.ac.at; |
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Corporate Author |
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Publisher |
Iop Publishing Ltd |
Place of Publication |
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Language |
English |
Summary Language |
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ISSN |
1751-8113 |
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Conference |
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Notes |
WOS:000316058200010 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1353 |
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Author |
Caroca, R.; Kondrashuk, I.; Merino, N.; Nadal, F. |
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Title |
Bianchi spaces and their three-dimensional isometries as S-expansions of two-dimensional isometries |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
22 |
Pages |
225201 - 24pp |
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Keywords |
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Abstract |
In this paper we show that certain three-dimensional isometry algebras, specifically those of type I, II, III and V (according to Bianchi's classification), can be obtained as expansions of the isometries in two dimensions. In particular, we use the so-called S-expansionmethod, which makes use of the finite Abelian semigroups, because it is the most general procedure known until now. Also, it is explicitly shown why it is impossible to obtain the algebras of type IV, VI-IX as expansions from the isometry algebras in two dimensions. All the results are checked with computer programs. This procedure shows that the problem of how to relate, by an expansion, two Lie algebras of different dimensions can be entirely solved. In particular, the procedure can be generalized to higher dimensions, which could be useful for diverse physical applications, as we discuss in our conclusions. |
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Address |
Univ Catolica Santisima, Dept Matemat & Fis Aplicadas, Concepcion, Chile, Email: nelson.merino@ucv.cl |
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Publisher |
Iop Publishing Ltd |
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Language |
English |
Summary Language |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
1751-8113 |
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Medium |
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Expedition |
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Conference |
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Notes |
WOS:000319044900004 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1457 |
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| Permanent link to this record |
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Author |
Andrianopoli, L.; Merino, N.; Nadal, F.; Trigiante, M. |
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Title |
General properties of the expansion methods of Lie algebras |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
36 |
Pages |
365204 - 33pp |
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Keywords |
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Abstract |
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow us to do so is called expansion of Lie algebras, and has been recently used in different physical applications-particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows us to check explicitly all our theoretical results is also provided. |
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Address |
[Andrianopoli, L.; Nadal, F.; Trigiante, M.] Politecn Torino, Dipartimento Sci Applicata & Tecnol DISAT, I-10129 Turin, Italy, Email: nelson.merino@ucv.cl |
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Corporate Author |
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Thesis |
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Publisher |
Iop Publishing Ltd |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1751-8113 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000323421800008 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1560 |
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| Permanent link to this record |
