We discuss a method to construct a De Rham complex (diierential algebra) of Poincar e-Birkhoo-Witt-type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a diierential Hopf algebra that naturally extends the Hopf algebra structure of U(g). The construction of such diierential structures is interpreted in terms of colour Lie superalgebras.

In this paper we consider the algebra (A, f, g), where f and g are m-ary and n-ary operations on the set A. We define the concept of regular algebra and we prove that for a regular medial algebra (A, f, g) there exists a commutative semigroup (A,+) such that the operations f and g have linear representations on (A,+). As a corollary, we show that for a regular medial algebra (A,F ) there exists...

Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g ⊕ g+, and let s and t be commuting formal variables commuting with g. We prove that the map C : sg[[s, t]] × tg+[[s, t]] −→ sg[[s, t]] ⊕ tg+[[s, t]] defined by the Campbell-Baker-Hausdorff formula and given by e − e + = eC(sg ,tg) for g ∈ g[[s, t]] is a bijection, as is well known when g ...

— In [Böh] a structure theorem for Gorenstein algebras in codimension 2 was obtained. In Section 1 of this article we give a geometric application and prove a structure theorem for good birational canonical projections of regular surfaces of general type with pg = 5 to P4 (Theorem 1.6). In Section 2 we show how this can be used to analyze the moduli space of canonical surfaces with q = 0, pg = ...

The Yangian Y (g) associated to a finite-dimensional complex simple Lie algebra g is a Hopf algebra deformation of the universal enveloping algebra of the Lie algebra g[u] of polynomial maps C → g (with Lie bracket defined pointwise). It is important to understand the finite-dimensional representations of Y (g). For one thing, they are closely related to rational solutions of the so-called quan...

In [2], A.Alekseev and E.Meinrenken construct an explicit G-differential space homomorphism Q, called the quantization map, between the Weil algebra Wg = S(g ) ⊗ ∧(g) and Wg = U (g) ⊗ Cl(g) (which they called the noncommutative Weil algebra) for any quadratic Lie algebra g. They showed that Q induces an algebra isomorphism between the basic cohomology rings H bas(Wg) and H ∗ bas(Wg). In this pa...

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V . In [DY], it was shown that any irreducible V -module is a completely reducible V module where V G is the G-invariant sub-vertex operator algebra of V . In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V...

For a locally compact group G, let A(G) denote its Fourier algebra and, for p ∈ (1,∞), let Ap(G) be the corresponding Figà-Talamanca–Herz algebra. For amenable G and p, p ∈ (1,∞) such that 1 p + 1 p , we show that Ap(G) ∩Ap′(G) = A(G).

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of C(X). We calculate the Hilbert polynomial of this algebra. In particular, we show that the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. We...

Let g be a Lie algebra over a field F of characteristic zero, let C be a certain tensor category of representations of g, and C a certain category of duals. By a Tannaka reconstruction we associate to C and C a monoid M with a coordinate ring of matrix coefficients F [M ] (which has in general no natural coalgebra structure), as well as a Lie algebra Lie(M). The monoid M and the Lie algebra Lie...