Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...

H. Weyl has defined a semi-simple algebra (of finite rank) to be an algebra which admits a faithful semi-simple linear representation. Now, algebras are rings with a field of operators; Artin and others have shown that the theory of semi-simple algebras can be generalized to a theory of semi-simple rings (without the field of operators) provided we replace the condition of finite rank by suitab...

In this paper we present our latest modular robot “MTRAN”(Modular Transformer) and its motion generation algorithm based on a four-module block method. The developed module is composed of two semi-cylindrical parts connected by a link. Each part has three connection surfaces where another module can be connected by magnetic force. Each module has only two degrees of freedom, but a group of modu...

There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.

We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports φ : Z → Spec(R) satisfies the weak Cousin condition if for any integer i the set φ(i) contains all the inmediate generalizations of each point in φ(i+ 1). Every t-structure on Dbfg(R) ...

By using properties of dualizing parametrization functions, Lagrangian functions and the epigraph technique, some sufficient and necessary conditions of the stable strong duality and strong total duality for a class of DC optimization problems are established.