相关论文: Solving the noncommutative Batalin-Vilkovisky equa…

Let E be an arbitrary graph, K be any field and let L be the corresponding Leavitt path algebra. Necessary and sufficient conditions (which are both algebraic and graphical) are given under which all the irreducible representations of L are…

We develop a noncommutative invariant theory for ordinary linear differential operators on Riemann surfaces. For a monic binomially normalized operator $L=\sum_{k=0}^n {n\choose k}a_kD^{\,n-k}$, $a_0=1$, with coefficients in an associative…

We present a concise method to construct a BRST invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution for the master equation is directly obtained by…

We give a conceptual formulation of Kontsevich's `dual construction' producing graph cohomology classes from a differential graded Frobenius algebra with an odd scalar product. Our construction -- whilst equivalent to the original one -- is…

The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…

Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how…

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these…

In this paper we analyse a certain type of higher derivative gauge theories which are known to possess BRST symmetry associated with their higher derivative structure. We first show that these theories are also invariant under a anti-BRST…

This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular,…

Using the Batalin-Vilkovisky formalism we provide a detailed analysis of the NS sector of boundary superstring field theory. We construct explicitly the relevant BV structure and derive the master action. Furthermore, we show that this…

We formalize the construction by Batalin and Vilkovisky of a solution of the classical master equation associated with a regular function on a nonsingular affine variety (the classical action). We introduce the notion of stable equivalence…

I review the construction of actions for extended geometry from the grading of an underlying tensor hierarchy algebra, which provides the full set of Batalin-Vilkovisky fields. The dynamics is neatly encoded in a complex. This talk,…

We use the fusion formulas of the symmetric group and of the Hecke algebra to construct solutions of the Yang-Baxter equation on irreducible representations of $\mathfrak{gl}_N$, $\mathfrak{gl}_{N|M}$, $U_q(\mathfrak{gl}_N)$ and…

We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging…

We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…

This paper considers a finite group $G$ acting linearly on the variables $V$ of a polynomial algebra, or an exterior algebra, or superpolynomial algebra with both commuting and anticommuting variables. In this setting, the Hilbert series…

We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$-dimensional $2$-handlebodies up to $1$-isotopy. In the process, we recover invariants due to Bobtcheva-Messia, Broda-Petit,…

We study the geometry of the Lagrangian Batalin--Vilkovisky theory on an antisymplectic manifold. We show that gauge symmetries of the BV-theory are essentially the symmetries of an even symplectic structure on the stationary surface of the…

This short note contains a combinatorial construction of symmetries arising in symplectic geometry (partially wrapped or infinitesimal Fukaya categories), algebraic geometry (derived categories of singularities), and K-theory (Waldhausen's…