Related papers: Deformations of Batalin-Vilkovisky algebras

New deformed affine algebras A_{\hbar,\eta}(\hat{g}) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A_{\hbar,\eta}(\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and Pakuliak (KLP).…

In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations,…

Let $n\ge 1$ and $A$ be a commutative algebra of the form $\boldsymbol k[x_1,x_2,\dots, x_n]/I$ where $\boldsymbol k$ is a field of characteristic $0$ and $I\subseteq \boldsymbol k[x_1,x_2,\dots, x_n]$ is an ideal. Assume that there is a…

This is a copy of the article published in IMRN (2007). I describe the noncommutative Batalin-Vilkovisky geometry associated naturally with arbitrary modular operad. The classical limit of this geometry is the noncommutative symplectic…

In this paper we generalize to associative superalgebras Gerstenhaber's work on cohomology structure of an associative algebra. We introduce two multiplications U and [-,-] on the cochain complex C^*(A;A) of an associative superalgebra A.…

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…

This paper examines (restricted) Koszul Lie algebras, a class of positively graded Lie algebras with a quadratic presentation and specific cohomological properties. The study employs HNN-extensions as a key tool for decomposing and…

This article explores \Z_2-graded L_\infinity algebra structures on a 2|1-dimensional vector space. The reader should note that our convention on the parities is the opposite of the usual one, because we define our structures on the…

We introduce the notion of a BV-operator $\Delta=\{\Delta^n:V^n\longrightarrow V^{n-1}\}_{n\geq 0}$ on a homotopy $G$-algebra $V^\bullet$ such that the Gerstenhaber bracket on $H(V^\bullet)$ is determined by $\Delta$ in a manner similar to…

We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…

It is shown that every $2$-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra $A$ defines a very explicit infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric monoidal…

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…

This article considers the structure and properties of $\delta$-Novikov algebras, a generalization of Novikov algebras characterized by a scalar parameter $\delta$. It looks like $\delta$-Novikov algebras have a richer structure than…

Given a central arrangement of lines $\mathcal{A}$ in a $2$-dimensional vector space $V$ over a field of characteristic zero, we study the algebra $\mathcal D(\mathcal A)$ of differential operators on $V$ which are logarithmic along…

A Baxter algebra is a commutative algebra $A$ that carries a generalized integral operator. In the first part of this paper we review past work of Baxter, Miller, Rota and Cartier in this area and explain more recent work on explicit…

We determine the Gerstenhaber structure on the Hochschild cohomology ring of a class of self-injective special biserial algebras. Each of these algebras is presented as a quotient of the path algebra of a certain quiver. In degree one, we…

The lattice vertex operator algebra $V_L$ associated to a positive definite even lattice $L$ has an automorphism of order 2 lifted from -1-isometry of $L$. We prove that for the fixed point vertex operator algebra $V_L^+$, any…

Let $M$ be a compact oriented $d$-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM)$. Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky…

If $Q$ is a non degenerate quadratic form on ${\bb C}^n$, it is well known that the differential operators $X=Q(x)$, $Y=Q(\partial)$, and $H=E+\frac{n}{2}$, where $E$ is the Euler operator, generate a Lie algebra isomorphic to ${\go…