In this paper we present an alternative proof for the existence theorem of the singular value decomposition in the extended max algebra and we propose some possible extensions of the max-algebraic singular value decomposition. We also prove the existence of a kind of QR decomposition in the extended max algebra.

Abstract Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus attention due to the fundamental rôle they play for extended geometry. In present paper, we examine tensor which super-extensions over-extended (often, hyperbolic...

A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of Heisenberg double construction is investigated for momenta generators. This leads to phase space model. Further, extended algebra constructed using algebra, in one dimension higher. dual pair group then formulated. Two doubles are considered, with conjugate tensorial anothe...