Irreducible representations of quantum matrices.
We present a description of irreducible tensor representations of general linear Lie superalgebras in terms of generalized determinants in the symmetric and exterior superalgebras of a superspace over a field of characteristic zero.
The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santilli?s isotheory. We study the isotopic liftings of groups and subgroups and we also deal with the differences between an isosubgroup and a subgroup of an isogroup. Finally, some links between this isotheory and the standard groups theory, referred to representation and equivalence relations among groups are shown.
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.