Related papers: On symplectic quandles

Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has…

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…

Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…

The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…

Let $G$ be a finite group and let $k$ be an algebraically closed field of characteristic $2$ and let $M$ be an indecomposable $kG$-module which affords a non-degenerate $G$-invariant symmetric bilinear form. We introduce the symmetric…

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…

We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…

In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cubic 4-fold which are obtained by Serre's construction from…

A basis for the space of generalized theta functions of level one for the spin groups, parameterized by the theta characteristics (the even theta characteristcs for the odd spin groups) on a curve, is shown to be projectively flat over the…

Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…

Let $R$ be an associative ring with identity. A unital right $R$-module $M$ is called strongly finite dimensional if Sup$\{{\rm G.dim} (M/N) | N\leq M\} < +\infty$. Properties of strongly finite dimensional modules are explored. It is also…

We are intereseted in quandles and their enveloping groups. Various results are proven. We show that a quandle $Q$ and its image in the enveloping group $G(Q)$ have isomorphic enveloping groups. The image quandle is injective. For $Q$ a…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic…

This work addresses some relevant characteristics and properties of $q$-generalized associative algebras and $q$-generalized dendriform algebras such as bimodules, matched pairs. We construct for the special case of $q=-1$ an…

The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain…