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Tangent Lie algebras to the holonomy group of a Finsler manifold

Zoltán Muzsnay, Péter T. Nagy (2011)

Communications in Mathematics

Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to...

Tempered groups.

Teichmann, Josef (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Tempered reductive homogeneous spaces

Yves Benoist, Toshiyuki Kobayashi (2015)

Journal of the European Mathematical Society

Let G be a semisimple algebraic Lie group and H a reductive subgroup. We find geometrically the best even integer p for which the representation of G in L 2 ( G / H ) is almost L p . As an application, we give a criterion which detects whether this representation is tempered.

Ternary symmetries and the Lorentz group

Richard Kerner (2011)

Banach Center Publications

We show that the Lorentz and the SU(3) groups can be derived from the covariance principle conserving a Z₃-graded three-form on a Z₃-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.

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