Invariant Theory for Generalized Root Systems.
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
The half-liberated orthogonal group appears as intermediate quantum group between the orthogonal group , and its free version . We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between and , a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that...
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.
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.