Related papers: Holomorphic Symplectic Fermions

Let H be the Taft algebra over a finite commutative ring R. When N is a unit in R, we show that all H-cleft extensions over R are determined up to H-comodule algebra isomorphism by their polynomial H-identities.

We construct a diagram D, indexed by a finite partially ordered set, of finite Boolean semilattices and (v,0,1)-embeddings, with top semilattice $2^4$, such that for any variety V of algebras, if D has a lifting, with respect to the…

With a non-unitary transformation, the Lagrangian of a Dirac fermion is decomposed into two decoupled sectors. We propose to describe massive relativistic fermions in gauge theories in a two-component form. All relations between the Green's…

We present a new formulation of the staggered fermion on the D-dimensional lattice based on the SO(2D) Clifford algebra, which is naturally present in the action. The action of the massless staggered fermion is invariant under the discrete…

H. Hertz called any manifold M with a given nonintegrable distribution {\it nonholonomic}. Vershik and Gershkovich stated and R. Montgomery proved that the space of germs of any nonholonomic distribution on M with an open and dense orbit of…

Let G be a connected reductive group acting on a finite dimensional vector space V. Assume that V is equipped with a G-invariant symplectic form. Then the ring C[V] of polynomial functions becomes a Poisson algebra. The ring C[V]^G of…

The notions of a cleft extension and a cross product with a Hopf algebroid are introduced and studied. In particular it is shown that an extension (with a Hopf algebroid $H= (H_L,H_R)$) is cleft if and only if it is $H_R$-Galois and has a…

This paper investigates ways to enlarge the Hamiltonian subgroup Ham of the symplectomorphism group Symp(M) of the symplectic manifold (M, \omega) to a group that both intersects every connected component of Symp(M) and characterizes…

We investigate the extension of the Prokof'ev-Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

Let $M$ be a holomorphic symplectic K\"ahler manifold equipped with a Lagrangian fibration $\pi$ with compact fibers. The base of this manifold is equipped with a special K\"ahler structure, that is, a K\"ahler structure $(I, g, \omega)$…

Electrons on honeycomb or pi-flux lattices obey effective massless Dirac equation at low energies and at the neutrality point, and should suffer quantum phase transitions into various Mott insulators and superconductors at strong two-body…

Let $(M,I, \Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $\pi:\; M \mapsto X$, and $\eta$ a closed form of Hodge type (1,1)+(2,0) on $X$. We prove that $\Omega':=\Omega+\pi^* \eta$ is…

Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a…

We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular,…

For an aspherical symplectic manifold, closed or with convex contact boundary, and with vanishing first Chern class, a Floer chain complex is defined for Hamiltonians linear at infinity with coefficients in the group ring of the fundamental…

Let $M$ be the moduli space of complex Lagrangian submanifolds of a hyperK\"ahler manifold $X$, and let $\varpi : \widehat{\mathcal{A}} \rightarrow M$ be the relative Albanese over $M$. We prove that $\widehat{\mathcal{A}}$ has a natural…

The division algebras R, C, H, O are used to construct and analyze the N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N=8 super-KdV system is introduced and shown to admit a Poisson bracket…