An action of the Yangian of the general linear Lie algebra glN is defined on every irreducible highest weight module of ĝlN with integer level > 2. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra H. Each vacuum module of ĝlN is decomposed into irreducible Yangian re...

We consider the GNS Hilbert space H of a uniformly hyper-finite C∗algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic cocycle, implemented by the Hudson-Parthasa...

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

We study the cohomology H(A) = Ext∗A(k, k) of a locally finite, connected, cocommutative Hopf algebra A over k = Fp. Specifically, we are interested in those algebras A for which H∗(A) is generated as an algebra by H(A) and H(A). We shall call such algebras semi-Koszul. Given a central extension of Hopf algebras F → A → B with F monogenic and B semiKoszul, we use the Cartan-Eilenberg spectral s...

The structure of arbitrary associative commutative unital artinian algebras is well-known: they are finite products of associative commutative unital local algebras [6, pg.351, Cor. 23.12]. In the semi-simple case, we have the Artin-Wedderburn Theorem which states that any semi-simple artinian algebra (which is assumed to be associative and unital but not necessarily commutative) is a direct pr...

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.

We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and the character for the action of the symmetric groups on their homology. We finally study the associated incidence Hopf algebra, which is similar to the Faà di Bruno Hopf algebra.

Suppose g to be a complex semi-simple Lie algebra. In 1955, Chevalley showed that one can assign to it an essentially unique Z-structure, with structure constants of a simple form, themselves unique up to some choices of sign. An algorithm to compute these is also due implicitly to Chevalley, explained explicitly in [Carter:1972] and more recently in [Cohen-Murray-Taylor:2004]. It is reasonably...

XML is becoming increasingly popular as a means of exchanging a wide variety of data on the web. It is anticipated that in the future, many websites will be built from XML documents. XML databases would be required to manage these websites and also provide a way for users to search their contents. In this paper we give an overview of the development of query algebras from the original relationa...

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.