The symmetric algebra of a (finite-dimensional) g-module V is the algebra of polynomial functions on the dual space V . Therefore one can study the algebra of symmetric invariants using geometry of G-orbits in V ∗ . In case of the exterior algebra, ∧•V, lack of such geometric picture results by now in absence of general structure theorems for the algebra of skew-invariants (∧•V)g . One may find...

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi-Yau if and only if the universal en...

Let G be a complex reductive algebraic group, g its Lie algebra and h a reductive subalgebra of g, n a positive integer. Consider the diagonal actions G : g, NG(h) : h . We study a relation between the algebra C[h]G and its subalgebra consisting of restrictions to h of elements of C[g].

We consider and study Blaschke inductive limit algebras A(b), defined as inductive limits of disc algebras A(D) linked by a sequence b = {Bk}k=1 of finite Blaschke products. It is well known that big G-disc algebras AG over compact abelian groups G with ordered duals Γ = Ĝ ⊂Q can be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b) is a maximal and Dirichl...

The purpose of this paper is to complete Getzler-Jones’ proof of Deligne’s Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and the Hochschild complex of an associative algebra. More concretely, it is shown that the B∞-operad, which is generated by multilinear operations known to act on the Hochschild complex, is a quotient ...

In this paper we show that the K-algebra (G, ·, , e) on an abelian group (G, ·) is equivalent to the p-semisimple BCI-algebra (G; , e). Mathematics Subject Classification: 06F35, 20A05.

Let G be a simple complex classical group and g its Lie algebra. Let U~(g) be the Drinfeld-Jimbo quantization of the universal enveloping algebra U(g). We construct an explicit U~(g)-equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.

Theorem 1. Let G ⊂ GL(n,R) be a real reductive group with Cartan decomposition g = k⊕ p, g being the Lie algebra of G. Let GC be the subgroup of GL(n,C) with Lie algebra g ⊕ ig and K̃ the subgroup of GC whose Lie algebra is k⊕ ip. Let ΩC be a complex homogeneous space for GC and φ a K̃-invariant strictly plurisubharmonic function on ΩC. If Ω is a G-orbit in ΩC and f = φ|Ω has a critical point, th...

Exercise [1.1.13] (a) Let G = ⋂ α Fα, with each Fα a σ-algebra. Since Fα a σ-algebra, we have that Ω ∈ Fα, and as this applies for all α, it follows that Ω ∈ G. Suppose now that A ∈ G. That is, A ∈ Fα for all α. Since each Fα is a σ-algebra, it follows that A ∈ Fα for all α, and hence A ∈ G. Similarly, let A = ⋃ iAi for some countable collection A1, A2, . . . of elements of G. By definition of ...