We extend the classical result asserting that twisting operator preserves certain Deligne–Lusztig character values for truncated formal power series; along way we discuss some properties of centralisers. Then, combining with orbit construction, apply it to analyse SL2 over finite dual numbers. In appendix an action GLn(Fq[[π]]/πr) on a Springer fibre intersected by varieties.

We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on G corresponds to a cluster structure in O(G). We have shown before that this conjecture holds for any G in the case ...

in this paper, we introduce a class of rings which is a generalization of reversible rings. let r be a ring with identity. a ring r is called central reversible if for any a,b ∈ r, ab=0 implies ba belongs to the center of r. since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. we prove that some results of reversible ri...

in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

The review is devoted to nonassociative algebras, rings and modules over them. main actual recent trends in this area are described. Works reviewed on radicals rings, algebras related with skew polynomials, commutative their modules, cyclic obtained as extensions, Ore extensions of hom-associative them, von Neumann finiteness for algebras. Furthermore, there outlined them harmonic analysis nonl...

An elegant and strong theory on noncommutative Noetherian rings has been developed in several groundbreaking works over the second half of the 20th century following the pioneering research of Alfred Goldie in the 1960s. The theory is still an active research area in Algebra and features many important classes of rings such as matrix rings, polynomial rings, differential operator rings, group r...

Abstract We introduce and study multivariate zeta functions enumerating subrepresentations of integral quiver representations. For nilpotent such representations defined over number fields, we exhibit a homogeneity condition that prove to be sufficient for local functional equations the generic Euler factors these functions. This generalizes unifies previous work on submodule including, specifi...

With the exception of the terminal benzene rings, the atoms in the title compound, C(20)H(18)ClN(3)O(2), are approximately coplanar (r.m.s. deviation = 0.0495 Å). The benzene/chloro-benzene rings form dihedral angles of 3.02 (4) and 41.59 (5)°, respectively, with this plane. The hy-droxy, amino and carbonyl groups all lie to the same side of the mol-ecule, enabling the formation of intra-molecu...

In infinite-dimensional Lie theory, the affine Kac-Moody algebras and groups play a distinguished role due to their many applications various areas of mathematics physics. Underlying these objects there are closely related group schemes finite type over Laurent polynomial rings. The language SGA3 is perfectly suited describe such objects. purpose this short article provide natural description u...