We show that some finite W-superalgebras based on gl(M |N) are truncation of the super-Yangian Y (gl(M |N)). In the same way, we prove that finite W-superalgebras based on osp(M |2n) are truncation of the twisted super-Yangians Y (gl(M |2n)) +. Using this homomorphism, we present these W-superalgebras in an R-matrix formalism, and we classify their finite-dimensional irreducible representations.

Let M be a compact, oriented, irreducible, and boundary incompressible 3–manifold. Assume that its fundamental group is without rank two abelian subgroups and ∂M 6= ∅. We will show that every homomorphism θ: π1(M )→ PSL(2,C) which is not “boundary elementary” is induced by a possibly branched complex projective structure on the boundary of a hyperbolic manifold homeomorphic to M . AMS Classific...

Given a homomorphism of commutative noetherian rings R → S and an S–module N , it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals sup {m ∈ Z | Torm(E,N) 6= 0}, where E is the injective hull of the residue field of R. This re...

We consider mappings between edge sets of graphs that lift tensions to tensions. Such mappings are called tension-continuous mappings (shortly mappings). Existence of a mapping induces a (quasi)order on the class of graphs, which seems to be an essential extension of the homomorphism order (studied extensively, see [10]). In this paper we study the relationship of the homomorphism and orders. W...

A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...

4.3. (i) Since HomA(A (I),M) ∼= M (I) for a set I and ⊕ is exact, it is clear that HomA(A (I),−) is exact, i.e. A(I) is projective. (ii) “Only if” part: Let A(P ) = ⊕ p∈P Ap be the free A-module indexed by P and ψ : A (P ) → p be the A-homomorphism such that ψ(1p) = p. Then ψ is surjective. If P is projective, then ψ has a section, i.e. an A-homomorphism φ : P → A(P ) such that ψ ◦ φ = idP . Th...

Let E be a vector lattice, $$\lambda _1,\lambda _2,\ldots ,\lambda _k$$ scalars and $$\varphi _1,\ldots ,\varphi pairwise independent regular linear functionals on E. We show that if $$k<m$$ then $$\sum _{j=1}^k\lambda _j\varphi _j^m$$ is orthogonally additive only _j$$ or $$-\varphi lattice homomorphism for each j, $$1\le j\le k$$ . Moreover, $$m\ge 2$$ , we provide an example to this result d...

Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...