The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.

In 1964, Weil gave a criterion for local rigidity of a homomorphism from a finitely generated group Γ to a finite dimensional Lie group G in terms of cohomology of Γ with coefficients in the Lie algebra of G. This note announces a generalization of Weil’s result to a class of homomorphisms into certain infinite dimensional Lie groups, namely diffeomorphism groups of compact manifolds. This give...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

In this work, by considering a class of matrix valued fuzzy controllers and using (?,?)-Cauchy–Jensen additive functional equation ((?,?)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, obtain existence unique solution H–U–R stability (Hyers–Ulam–Rassias) for homomorphisms Jordan on Lie algebras with ? members (?-LMVFA). With regards to ea...

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Abstract Using crossed homomorphisms, we show that the category of weak representations (respectively admissible representations) Lie–Rinehart algebras Leibniz pairs) is a left module over monoidal Lie algebras. In particular, corresponding bifunctor categories established to give new pairs). This generalises and unifies various existing constructions many by using this bifunctor. We construct ...