The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N+, N−) are provided. They generalize the Virasoro and W∞ algebras to higher dimensions. The connection with volumepreserving diffeomorphisms on M , higher generalized-spin and tensor operator algebras of U(N+, N−) is discussed. These centrally-extended, infinite-...

In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra \(C^{(1)}_\ell\), \(\ell\geq2\), and similar with no obvious connection representation theory algebras.

let $mathcal{a}$ and $mathcal{b}$ be two $c^{*}$-algebras such that $mathcal{b}$ is prime. in this paper, we investigate the additivity of maps $phi$ from $mathcal{a}$ onto $mathcal{b}$ that are bijective, unital and satisfy $phi(ap+eta pa^{*})=phi(a)phi(p)+eta phi(p)phi(a)^{*},$ for all $ainmathcal{a}$ and $pin{p_{1},i_{mathcal{a}}-p_{1}}$ where $p_{1}$ is a nontrivial projection in $mathcal{a...

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie structure together with the Leibniz law. The non-commutative Poisson algebra structures on the infinite-dimensional algebras are studied. We show that these structures are standard on the poset subalgebras of the associative algebra of all endomorphisms of the countable-dimensional vector space T...

This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld and generalizes the results of [BFGP] and [BP]. In the second part we apply our techniques of quan-tization to obtain some nontrivial examples of quantization of Pois...

Analogue to commutants in the theory of associative algebras, one can construct a new subalgebra of vertex algebra known as a vertex algebra commutant. In this paper, for the adjoint representation V of Lie algebra sl(2,C), we describe a commutant of βγSystem S(V ) by giving its generators, moreover, we get a new Howe pair of vertex algebras.

We prove that every finitely generated Lie algebra containing a nilpotent ideal of class c and finite codimension n has Gelfand-Kirillov dimension at most cn. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.

We integrate the Lifting cocycles Ψ2n+1,Ψ2n+3,Ψ2n+5, . . . ([Sh1], [Sh2]) on the Lie algebra Difn of holomorphic differential operators on an n-dimensional complex vector space to the cocycles on the Lie algebra of holomorphic differential operators on a holomorphic line bundle λ on an n-dimensional complex manifold M in the sense of Gelfand–Fuks cohomology [GF] (more precisely, we integrate th...

The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is, similarly, related to Hochschild homology [C, L]. For a Lie algebra g this new theory is the homology of the complex C,(g) ... ~ ~| g|-+ ... ~1 ~ k, whose boundary map d is given by the formula d(gl|1...

Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius algebras in C. Such an algebra A encodes all data needed to ensure the existence of correlators of a local conformal field theory. The Picard group of the ca...