We give a sufficient criterion on a highest weight module of a semisimple Lie algebra to admit a resolution in terms of sums of modules induced from a parabolic subalgebra. In particular, we show that all unitary highest weight modules admit such a resolution. As an application of our results we compute (minimal) resolutions and explicit formulas for the Hilbert series of the unitary highest we...

Let L be a finite-dimensional, semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let H be a fixed Cartan subalgebra of L, and Φ be the root system. Fix a base ∆ = {α1, · · · , αl} of Φ. Let Λ denote the set of dominant, integral linear functions on H. Theorem 0.1. There is a one-to-one correspondence Λ ∼ −→ {isomorphism classes of finite-dimensional irreducible L-...

A new class of associative algebras is introduced and studied. These algebras are related to simple complex Lie algebras (or root systems). Roughly speaking, they are finite dimensional approximations to the enveloping algebra U(g) viewed as a module over its center. It seems that several important questions on semisimple algebras and their representations can be formulated, studied and sometim...

A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a quotient space of an open subset of a vector space V by a quasitorus action and on investigation ...

The activation of carbon monoxide by oxygen on Mg(100) surface has been investigated by X-ray photoelectron spectroscopy (XPS). Carbon monoxide is only weakly adsorbed (dispersion-type forces) on a magnesium surface. The XPS result has shown that the dissociation of carbon monoxide leading to the formation of a metastable surface carbonate species occurs through the participation of an oxyg...

the activation of carbon monoxide by oxygen on mg(100) surface has been investigated by x-ray photoelectron spectroscopy (xps). carbon monoxide is only weakly adsorbed (dispersion-type forces) on a magnesium surface. the xps result has shown that the dissociation of carbon monoxide leading to the formation of a metastable surface carbonate species occurs through the participation of an oxygen s...

1. Preliminaries. Let X be the class of compact 1 connected semisimple Lie groups; 3C'C3C is the following set of groups, Sp(w), SU(w), Spin(w), G2, F*, EQ, E7, Es, U*(X) the weakly complex bordism of X [ l ] and A the ring U*(pt) = Z[Fi , F2, • • • ]. A is the weakly complex bordism ring defined by Milnor. The generators F,are weakly complex manifolds of dim 2i. The bordism class of a weakly c...

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...

We show that actions of finite-dimensional semisimple commutative Hopf algebras H on //-module algebras A are essentially group-gradings. Moreover we show that the centralizer of H in the smash product A # H equals A" ® H. Using these we invoke results about group graded algebras and results about centralizers of separable subalgebras to give connections between the ideal structure of A, A and ...