Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with cocommutative Hopf algebra structure. We show that if L is a primitive pseudoalgebra over then all finite irreducible L' Cur_H^{H'} L-modules are of form V, where V an L-module, single class exceptions. Indeed, when H(d, \chi, \omega), we introduce non current L'-...

Abstract We use [11] to study the algebra structure of twisted cotriangular Hopf algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a $2$-cocycle for connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we show that ${}_J\mathcal{O}(G)_{J}$ an affine Noetherian domain with Gelfand–Kirillov dimension $\dim (G)$, and if unipotent supported on $G$, then ${}_J\mathcal{O}(G)_{J}\co...

Abstract Let $R$ be a positively graded finitely generated $\textbf {k}$-domain with Krull dimension $d+1$. We show that there is homogeneous valuation ${\mathfrak {v}}: R \setminus \{0\} \to {\mathbb {Z}}^d$ of rank $d$ such the associated $\operatorname {gr}_{\mathfrak {v}}(R)$ generated. This then implies any polarized $d$-dimensional projective variety $X$ has flat deformation over ${\mathb...

‎‎Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

In this paper we investigate certain aspects of infeasibility in convex integer programs. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining feasible region. We prove that for the considered class of convex functions, every infeasible system of inequality constraints in the convex integer pro...

Algorithms and computer-based tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixed-integer or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isolation of an Irreducible Infeasible Set of constraints (IIS), a subset of the constraints defining ...

If there exists a nonempty, proper subset S of the set of all (n+ 1)(n+ 2)/2 inertias such that S ⊆ i(A) is sufficient for any n×n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [Kim, Olesky and Driessche, Criti...

In [1], Eisenberg and Faltings proposed a breakout [2] based hybrid approach to detect infeasible subset (IS) in constraint satisfaction problems. In this paper, we adopted this algorithm as a preprocessing procedure to reduce the over-constrained constraint satisfaction problem. Then a three procedures hybrid approach is employed to detect the irreducible infeasible subset (IIS) of identified ...

We study the quotient of $\mathcal{T}_n = Rep(GL(n|n))$ by tensor ideal negligible morphisms. If we consider full subcategory $\mathcal{T}_n^+$ $\mathcal{T}_n$ indecomposable summands in iterated products irreducible representations up to parity shifts, its is a semisimple tannakian category $Rep(H_n)$ where $H_n$ pro-reductive algebraic group. determine connected derived subgroup $G_n \subset ...