We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements i...

Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X] in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the invariant ring need not be finitely generated. For this case, we develop an algorithm which computes K[X] in terms of a so-called colon-operation...

In this paper, a novel approach for finite-time stabilization of uncertain affine systems is proposed. In the proposed approach, a fast terminal sliding mode (FTSM) controller is designed, based on the input-output feedback linearization of the nonlinear system with considering its internal dynamics. One of the main advantages of the proposed approach is that only the outputs and external state...

It is proved that the Lie groups E (5) 7 and E (7) 7 represented in R 56 and the Lie group E C 7 represented in R 112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connnections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension. §1 Introduction The ...

A number of results are proved concerning the Quillen ^-theory K+(S*G) of the skew group ring S*G, where S is a Noetherian ring and G is a finite group of automorphisms of 5. Applications are given to the computation of AT-groups of group algebras and of equivariant /^-theory for affine varieties.

Let G be a finite non-regular primitive permutation group on set Ω with point stabiliser Gα. Then is said to extremely if Gα acts primitively each of its orbits in \ {α}, which notion dating back work Manning the 1920s. By theorem Mann, Praeger and Seress, it known that every either almost simple or affine, all examples have subsequently been determined. Similarly, Mann et al. classified affine...

The semi-affine Coxeter-Dynkin graph is introduced, generalizing both the affine and the finite types. Semi-affine graphs. It is profitable to treat the so-called Coxeter-Dynkin diagrams as graphs. A classification of finite graphs with an adjacency matrix having 2 as the largest eigenvalue is made in a paper of John Smith [JHS]. It is in a combinatorial context and no reference is made to Coxe...

If V is an affine algebraic variety and G ⊂ AutV a finite group of automorphism of V , the quotient variety is an affine algebraic variety V/G with a quotient morphism V → X = V/G. A point of X is an orbit of G on V , and the coordinate ring k[X] is the ring of invariants k[V ] of the induced action of G on k[V ]. This chapter studies the simplest case of this construction, when V = C and G = Z...

The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [BDD+90], and their classification has recently been completed (see [Lie98] and [Sax02]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears a variety of known examples. Here we giv...