We construct an $L_\infty$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to universal central extension Lie algebra Hamiltonian vector fields.

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...

For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic c...

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every topological space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1 in that all its elements satisfy the topological inter...

Non-highest weight representations of the current algebra so(1, n), and Laplace Operators. Abstract We constructed canonical non-highest weight unitary irreducible representation of so(1, n) current algebra as well as canonical non-highest weight non-unitary representations, We constructed certain Laplacian operators as elements of the universal enveloping algebra, acting in representation spac...

The notion of anyonic Wick algebras is introduced and the corresponding second quantisation procedure is discussed. Applications to the physics of 2D anyonic matter are presented. In particular the existence of thermodynamics in the infinite volume for the case of LeinaasMyrheim potentials is presented. Additionally a new class of states corresponding to quasifree thermal states on some Wick al...

We develop algebraic methods for finding loop corrections to the N = 4 SYM dilatation generator, within the noncompact psu(1, 1|2) sector. This sector gives a ’t Hooft coupling λ-dependent representation of psu(1, 1|2)× psu(1|1)2. At first working independently of the representation, we present an all-order algebraic ansatz for the λ-dependence of this Lie algebra’s generators. The ansatz solve...

Frequently one attaches to an arithmetic object a zeta function whose analytic behavior reflects deep properties of the object. For example, attached to Q there is the Riemann zeta function, whose behavior (especially the position of its zeros) contains information about the distribution of the prime numbers. Dedekind attached a zeta function to every algebraic number field, and Hasse and Weil ...