相关论文: Reduction of branes in generalized complex geometr…

We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite dimensional), then the Hopf envelope of…

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…

We extend the homological method of quantization of generalized Drinfeld--Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.

Motivated by the study of the structure of algebraic actions the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X $\rightarrow$ X//Ga restrict to principal homogeneous…

On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

In this paper we present simplifying techniques which allow one to compute the quiver diagrams for various D-branes at (non-Abelian) orbifold singularities with and without discrete torsion. The main idea behind the construction is to take…

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…

We establish a new universal relation between the Lie bracket and $\circ$-multiplication of tangent fields on any Frobenius (super)manifold. We use this identity in order to introduce the notion of ``weak Frobenius manifold'' which does not…

We study coisotropic submanifolds of $b$-symplectic manifolds. We prove that $b$-coisotropic submanifolds (those transverse to the degeneracy locus) determine the $b$-symplectic structure in a neighborhood, and provide a normal form…

We introduce the class of generalized biserial quiver algebras and prove that they provide a complete classification of all weakly symmetric biserial algebras over an algebraically closed field.

We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case. The…

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…

We introduce group graded basic Morita equivalences between algebras deter- mined by blocks of normal subgroups, and by using the extended Brauer quotient, we show that they induce graded basic Morita equivalences at local levels.

We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures…

We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…

We define Lie and Courant algebroids on Fr\'{e}chet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fr\'{e}chet manifold and show that it inherits a Fr\'{e}chet Lie algebroid structure. We show…