We give a coadjoint orbit's diffeomorphic deformation between the classical semisimple case and semi-direct product given by Cartan decomposition. The two structures admit Hermitian symplectic form defined in complex Lie algebra. provide some applications such as constructions of Lagrangian submanifolds.

<abstract><p>Let $ G be a graph with vertex set V(G) $. A function f:V(G)\rightarrow \{0, 1, 2\} is Roman dominating on if every v\in for which f(v) = 0 adjacent to at least one u\in such that f(u) 2 The domination number of the minimum weight \omega(f) \sum_{x\in V(G)}f(x) among all functions f In this article we study direct product graphs and rooted graphs. Specifically, give sev...

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...

The noncanonical Hamiltonian formulation of a recently derived four-field model describing collisionless reconnection is presented. The corresponding Lie-Poisson bracket is shown to be a sum of a direct and semi-direct product forms and to possess four infinite independent families of Casimir invariants. Three out of four of these families are directly associated with the existence of Lagrangia...

Solution. The 11-Sylow subgroup is Z/11Z; the 5-Sylow subgroup is Z/5Z. By Sylow’s theorem, the 11-Sylow subgroup is normal. Hence, the group is a semi-direct product of its 5 and 11-Sylow subgroups. Since Aut(Z/11Z) = Z/10Z has a unique subgroup of order 5, there are up to isomorphism exactly two groups of order 55: the abelian group Z/55Z and the group with presentation ⟨x, y|x = y = 1, xyx−1...

We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic subgroupoids and provide a groupoid presentation. In order to established the latter result, we describe quasi-centralizers in Garside groups. All results h...

We study a q-deformation for the semi-direct product of the symmetric group Sn with the Clifford algebra on n anticommuting generators. We obtain a q-version of the projective analogue for the classical Young symmetrizer introduced by the second author. Our main tool is an analogue of the Hecke algebra of complex valued functions on the group GLn over a p-adic field relative to the Iwahori subg...

The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive graded composition law and permits the introduction of Lie algebras over such aperiodic point sets. These infinite dimensional Lie algebras are shown to be repres...