Related papers: The Clifford Algebra Bundle on Loop Space
We determine the structure of the $*$-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra…
We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials,…
We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as…
A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…
Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e.…
The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…
Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…
The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and…
We use rudiments of the Seiberg-Witten gluing theory for trivial circle bundles over a Riemann surface to relate de Seiberg-Witten basic classes of two $4$-manifolds containing Riemann surfaces of the same genus and self-intersection zero…
We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we study the Calabi-Yau case, in which an…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…
In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…
We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.
The geometry of nonholonomic bundle gerbes, provided with nonlinear connection structure, and nonholonomic gerbe modules is elaborated as the theory of Clifford modules on nonholonomic manifolds which positively fail to be spin. We explore…
We consider a pair of independent scalar products, one scalar product on vectors, and another independent scalar product on dual space of co-vectors. The Clifford co-product of multivectors is calculated from the dual Clifford algebra. With…
We discuss various lifting and reduction problems for bundles and gerbes in the context of a strict Lie 2-group. We obtain a geometrical formulation (and a new proof) for the exactness of Breen's long exact sequence in non-abelian…
We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a…