相关论文: Berglund-H\"ubsch mirror symmetry via vertex algeb…
We give an explicit description of the BPS Lie algebra of any quiver with zero potential, by relating the perverse filtration on the cohomological Hall algebra with certain limit conditions on polynomials. Our results also give a partial…
We study the homological mirror symmetry statement where A-side is the conic bundle Hori--Vafa mirror $\mathcal{Y} = \{uv = f(z)\} \subset \mathbb{C}^2 \times (\mathbb{C}^\ast)^n$ for a Laurent polynomial $f$ in $(\mathbb{C}^\ast)^n$, and…
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly…
In this work we find the first examples of (0,2) mirror symmetry on compact non-K\"ahler complex manifolds. For this we follow Borisov's approach to mirror symmetry using vertex algebras and the chiral de Rham complex. Our examples of (0,2)…
There is a strange duality between the quadrangle isolated complete intersection singularities discovered by the first author and C.T.C.Wall. We derive this duality from the mirror symmetry, the Berglund-H\"ubsch transposition of invertible…
An alternative proof of bornological Verdier duality for complex manifolds, as proven initially by Prosmans & Schneiders is given, using Schneider's theory of quasi-abelian homological algebra, and the theory of residues and duality.
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach…
We consider the Berglund-H\"ubsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the…
We give an expository discussion of recent work using Berglund-Huebsch-Krawitz mirror symmetry to describe the structure of point counts on algebraic varieties over finite fields.
Let $\mathbf{U}$ be the quantized enveloping algebra and $\dot{\mathbf{U}}$ its modified form. Lusztig gives some symmetries on $\mathbf{U}$ and $\dot{\mathbf{U}}$. Since the realization of $\mathbf{U}$ by the reduced Drinfeld double of the…
It is shown that projectivized irreducible components of nilpotent cones of complex symmetric spaces are projective self-dual algebraic varieties. Other properties equivalent to their projective self-duality are found.
The main goals for this paper is i) to study of an algebraic structure of $\mathbb{N}$-graded vertex algebras $V_B$ associated to vertex $A$-algebroids $B$ when $B$ are cyclic non-Lie left Leibniz algebras, and ii) to explore relations…
Jake Goodman and Ulrich Kr\"ahmer have recently shown that a twisted Calabi-Yau algebra $A$ with modular automorphism $\sigma$ and dimension $d$ can be "untwisted," in the sense that the Ore extensions $A[X;\sigma]$ and $A[X^{\pm1};\sigma]$…
For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces.…
We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of…
The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula due to Hagen and…
In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without…
We modify the definition of the families of $A$ and $B$ stringy cohomology spaces associated to a pair of dual reflexive Gorenstein cones. The new spaces have the same dimension as the ones defined in the joint paper with Mavlyutov…
Let $V$ be a vertex algebra of countable dimension, $G$ a subgroup of ${\rm Aut} V$ of finite order, $V^{G}$ the fixed point subalgebra of $V$ under the action of $G$, and ${\mathscr S}$ a finite $G$-stable set of inequivalent irreducible…
A higher dimensional analogue of the notion of vertex algebra is formulated in terms of formal variable language with Borcherds' notion of $G$-vertex algebra as a motivation. Some examples are given and certain analogous duality properties…