Expansions of Algebras and Superalgebras and Some Applications

Azcárraga, J. A. de; Izquierdo, José M.; Picón, Moisés; Varela, Oscar

doi:10.1007/s10773-007-9385-3

Cited by 79 publications

(100 citation statements)

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“…In order to get a smaller algebra 4 we also demand (ii) that it contains a decomposition like that given in (12) which is resonant, i.e., that satisfies equation (6).…”

Section: The Type III Algebramentioning

confidence: 99%

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Bianchi spaces and their three-dimensional isometries asS-expansions of two-dimensional isometries

Caroca¹,

Kondrashuk²,

Merino³

et al. 2013

J. Phys. A: Math. Theor.

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In this paper we show that some 3-dimensional isometry algebras, specifically those of type I, II, III and V ( according Bianchi's classification), can be obtained as expansions of the isometries in 2 dimensions. It is shown that in general more than one semigroup will lead to the same result. It is impossible to obtain the algebras of type IV, VI-IX as an expansion from the isometry algebras in 2 dimensions. This means that the first set of algebras has properties that can be obtained from isometries in 2 dimensions while the second set has properties that are in some sense intrinsic in 3 dimensions. All the results are checked with computer programs. This procedure can be generalized to higher dimensions, which could be useful for diverse physical applications.

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“…In order to get a smaller algebra 4 we also demand (ii) that it contains a decomposition like that given in (12) which is resonant, i.e., that satisfies equation (6).…”

Section: The Type III Algebramentioning

confidence: 99%

“…[1], [2], [3], [4], [5], [6], [7]. These methods, in particular the S-expansion procedure developed in ref.…”

Section: Introductionmentioning

confidence: 99%

Bianchi spaces and their three-dimensional isometries asS-expansions of two-dimensional isometries

Caroca¹,

Kondrashuk²,

Merino³

et al. 2013

J. Phys. A: Math. Theor.

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“…3 Here and in the following, the quantities with a "tilde" symbol above will refer to quantities of the target (super)algebra. 4 A process which involves only resonance would be a simpler one, and it will be briefly treated in the following. Since we can factorize the zero element, the above relation can be simply rewritten as…”

Section: )mentioning

confidence: 99%

An analytic method forS-Expansion involving resonance and reduction

et al. 2016

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In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0 S -resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras.This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras.We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature. * marcalderon@udec.cl †

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“…[26][27][28][29]) in terms of better known procedures (Lie algebra expansion, see Refs. [30][31][32][33]). …”

Section: Gwzw Term and Maxwell Algebramentioning

confidence: 99%