On Natural Superhomogeneous Models for Minkowski Superspacetime

Peniche, R.; Salgado, G.; Sánchez-Valenzuela, O. A.

doi:10.1007/s00023-010-0023-x

Cited by 2 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our motivation for studying such Lie superalgebras is that 2 ⊂ 2 is a real form that can be identified with Minkowski spacetime, which is of interest in physical applications [10]. The Lie superalgebras of the form 2 ⊕ 1 , yield automorphism groups which become natural candidates for the superLorentz groups.…”

Section: Introductionmentioning

confidence: 99%

Lie Superalgebras Over 𝔤𝔩₂

Salgado

Sánchez-Valenzuela

2011

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

Finite-dimensional real and complex Lie superalgebras having either 2 or 2 = I 2 ⊕ 2 as their underlying even Lie algebra 0 , are classified up to isomorphism. It is shown that the number N of nonisomorphic Lie superalgebras defined in = 0 ⊕ V associated to a given representation 0 → V only depends on the multiplicities of the irreducible modules of dimensions 1, 2, and 2 + 1, when 0 = 2 ; if 0 = 2 , it depends only on the multiplicities of the irreducible modules of dimensions 1, 2, and 3. In dealing with any finite-dimensional representation 2 → V , the representation space V can be decomposed in the form V 1 ⊕ V 2 , with a completely reducible V 1 associated to diagonal Jordan blocks of I 2 , and a noncompletely reducible V 2 associated to nondiagonal Jordan blocks of I 2 . It is then proved that the given classification only depends on the representation in V 1 . The question of which isomorphism classes admit invariant orthogonal-like geometric structures is also settled; in other words, it is determined which superalgebras studied in this work are quadratic in the sense of [2]. It is shown in particular that the only quadratic Lie superalgebra of the form 2 ⊕ V is 1 2 .

show abstract

Section: Introductionmentioning

confidence: 99%