For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

For Gorenstein quotient spaces C d =G, a direct generalization of the classical McKay correspondence in dimensions d 4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstei...

Adversity quotient is the capacity to adjust with the adversities in life. A person with good Adversity quotient can achieve the goal by fighting against all odds. It is also related to many other factors like self esteem, motivation, fighting spirit, creativity, sincerity, positive attitude, optimism, emotional stability etc. Adversity quotient is also related to the Academic problems of stude...

We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G, P ), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica spectrum of (G, P ). Our original motivation and our main examples are drawn from right-angled Artin groups, but many of our results are valid for more gener...

conclusions chronic and moderate malnutrition did not influence the cognitive function, the intelligence quotient, and the impulsivity index. background undernutrition is the most common cause of growth retardation in developing countries. we aimed to assess the effect of undernutrition on cognition, intelligence quotient, and impulsivity index of 7-11 year-old children in shiraz, southern iran...

This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

In a recent paper,1 K. Asano gave a new proof of the theorem that a domain of integrity has a right quotient ring if and only if every pair of nonzero elements has a common nonzero right multiple. His method of proof is used in the present work to extend the centralizer of a ring over a module to a system of semi-endomorphisms of the module. From this extension, necessary and sufficient conditi...